Units

How to specify units

Units are a unique, inherent and simple feature of the z^3 language.

Using units is simple and easy. For example:

a=1m;

indicates that a is now a variable containing the value of 1 meter. For more complex units we can enclose them in brackets as in 3(m/sec).

If a variable needs to be specified in specific units, simply use the <> operator. Such as: a<>(m/sec);

In z^3 language, <> is the unit conversion operator. Also, any arithmetic operator such as +, -, *, /, ^, % etc. should be enclosed within < and > to allow unit conversions to propagate through these operations. These conversion operations can be done on arrays as parameters also. Hence to add a meter to 2 centimeters, do the following: a=1m<+>2cm; and z^3 will give the answer: 102 cm.

Note, that this result now carries the units with it for further operations. For example: a=(1m<+>2cm)<^>3; gives the answer as 1061208 cm3.

To convert the current value of a variable to a different unit, simply use the <> operator: a<>cm;

Notice that if a already had a unit, it will be appropriately converted using the units. If it did not have units inherently, it will simply be given the units.

a=1

1

a<>cm;

1 cm.

a=1m;

1 m.

a<>cm;

100 cm.

In the second case, 1m is converted to 100cm.

Variables with units can be operated on with or without unit awareness. The unit aware operators are enclosed in angular brackets and are listed in Unit Operators.

Unit Prefixes

Similarly, scales such as milli, mega, etc. are supported using conventional SI units.

a=1m;

1 m.

a<>ym;

1.0000000000000001e+24 ym.

Here a now has the unit yoctometer.

Using uppercase Y, we get the answer in Yottameter.

a=1m;

1 m.

a<>Ym;

1.0000000000000001e-24 Ym.

These conversions of scale follow the SI unit prefix standards.

Conversion among Unit Systems

z^3 supports conversion among unit systems, such as SI Units and FPS systems.

For example:

a=1mi;

1 mi.

a<>km;

1.6093439999999999 km.

Notice that the mi (miles) unit of variable a is converted to km.

Units on Array of Values

Units work on variables as simple numerical values or as arrays.

Let us consider numbers 1 to 10.

a=1..10;

Then say this is in miles.

b=a<>(mi);

Convert to kilometers.

b<>km

Numeric	Units	UNITSOF
1mi	km	1.6093439999999999km
2mi	km	3.2186879999999998km
3mi	km	4.828031999999999km
4mi	km	6.4373759999999995km
5mi	km	8.046719999999999km
6mi	km	9.656063999999999km
7mi	km	11.265407999999999km
8mi	km	12.874751999999999km
9mi	km	14.484096km
10mi	km	16.093439999999998km

We can convert arrays of Unit values to converted values as in the following:

a=(1..10)<>℃;

b=a<>℉;

Numeric	Units	UNITSOF
1℃	degF	33.8℉
2℃	degF	35.6℉
3℃	degF	37.4℉
4℃	degF	39.2℉
5℃	degF	41℉
6℃	degF	42.8℉
7℃	degF	44.6℉
8℃	degF	46.4℉
9℃	degF	48.2℉
10℃	degF	50℉

Units inside functions

Units can be highly effective inside functions. These, along with constants, provide a fantastic way to express your logic beautifully.

Let us consider how we can write E=mc^2. E:=(m<>kg)<*>(SPEEDOFLIGHT()<^>2);

E(2kg)

gives: 179751035747363520kg.m2.s-2

Note the use of <*> and <^> for the operators in unit operations.

In case you wanted to give the output in Joules.

E(2kg)<>J

gives: 179751035747363520J

Let us add variables intermixing miles and kilometer.

a=1mi;

b=10km;

[a,b,(a<+>b)<>mi]

[a,b,(a<+>b)<>mi]

1mi

10km

7.21371192237334mi

10mi<>km

can convert miles to kilometers.

Units Aware Internal Functions

In most sytems, functions like SIN operate on radians. Most users are unaware of this, and get confused when they get SIN(90) to be something unexpected.

With z^3 unit aware functions, this is not an issue.

For example,

a=90deg;

SIN(a)

will automatically convert the variable a into radians before calculations. To see the difference, try SIN(90) vs. SIN(90<>deg).

The answers given are: 0.8939966636005579 and 1.

Unit awareness is built into functions in z^3. (Note: Some functions are being transitioned).

Generation of Arrays with Units

rad2piby10

0㎭

0.6283185307179586㎭

1.2566370614359172㎭

1.8849555921538759㎭

2.5132741228718345㎭

3.141592653589793㎭

3.7699111843077517㎭

4.39822971502571㎭

5.026548245743669㎭

5.654866776461628㎭

6.283185307179586㎭

Note the results from rad2piby10 is automatically in radians.

Similarly array results using series in degrees are also marked with units of degrees.

deg110by10

0°

10°

20°

30°

40°

50°

60°

70°

80°

90°

100°

110°

(rad2piby10)<>rad<>deg

Numeric	Units	UNITSOF
0㎭	deg	0°
0.6283185307179586㎭	deg	36°
1.2566370614359172㎭	deg	72°
1.8849555921538759㎭	deg	108°
2.5132741228718345㎭	deg	144°
3.141592653589793㎭	deg	180°
3.7699111843077517㎭	deg	216°
4.39822971502571㎭	deg	252°
5.026548245743669㎭	deg	288°
5.654866776461628㎭	deg	324°
6.283185307179586㎭	deg	360°

shows the series in radians converted to degrees.

Currency Conversions

z^3 can automatically convert currencies.

b=(100$<+>3020¢);

gives the result

13020 cent.

b<>$;

gives

130.2 dollar.

With internal and external mappings to currency conversion dates, z^3 is able to do international currency conversions also.

(100..1000..100)<>USD<>INR

Numeric	Units	UNITSOF
100USD	INR	6680.820948336871INR
200USD	INR	13361.641896673742INR
300USD	INR	20042.462845010614INR
400USD	INR	26723.283793347484INR
500USD	INR	33404.10474168436INR
600USD	INR	40084.92569002123INR
700USD	INR	46765.7466383581INR
800USD	INR	53446.56758669497INR
900USD	INR	60127.388535031845INR
1000USD	INR	66808.20948336872INR

We can override internal conversion rates by using SETCONVERSION.

SETCONVERSION(1<>euro,1<>dollar,1.1)

PRINTCONVERSION();

can give the recently set conversion rates.

1<>€<>$

gives 1 euro to convert to 1$.

SETCONVERSION(1$,1€,0.9);

shows the following on PRINTCONVERSION(): {

  dollar:euro: 0.9,
  euro:dollar: 1.1111111111111112

}

Adding currencies is demonstrated further below:

(100$<+>300¢<+>30¢)<>$

gives:

103.3 dollar.

Array Unit Normalization

If an array holds a set of values from varied units, UNITIFY can convert all of them to the same units.

UNITIFY([1cm,2m,3cm])

will give: 1cm 200cm 3cm

Likewise: SUM(UNITIFY([1m,2m,3mm]))

will give the answer:

3.003 m.

SUM(UNITIFY([1m,2m,3mm]))<>cm

will give answer in cm :

300.3cm

PMT(4%,12,1000$,1200¢,0)

gives the result as:

-107.35079875828919 dollar.

since PMT is a unit aware function.

A gallon is converted to liter below.

1gal<>l

3.786235392 l.

A liter is converted to oz. below:

1<>l<>oz

33.806667242732274 oz.

Shown below are conversions to micro liters.

(1..10)<>l<>ul

Numeric	Units	UNITSOF
1l	ul	999999.9999999999ul
2l	ul	1999999.9999999998ul
3l	ul	2999999.9999999995ul
4l	ul	3999999.9999999995ul
5l	ul	4999999.999999999ul
6l	ul	5999999.999999999ul
7l	ul	6999999.999999999ul
8l	ul	7999999.999999999ul
9l	ul	8999999.999999998ul
10l	ul	9999999.999999998ul

Unit Aware Logical Operations

Unit aware variables and arrays can also be operated on with Unit Aware Logical Operators and Unit Aware Mathematical Operators. Such operators are listed in Unit_Operators.

Is 1m greater than 1cm?

1m<>>1cm;

true

Is 1m greater than 1cm, and is 2m greater than 200cm?

[1m,2m]<>>[1cm,200cm];

Answer is:

[true, false]. Note that an array of answers is obtained here.

Is 1m greater than or equal to 1cm, and is 2m greater or equal to than 200cm?

[1m,2m]<>=>[1cm,200cm];

Answer is:

[true, true].

Is 1m less than 1cm, and is 2m less than 200cm?

[1m,2m]<<>[1cm,200cm];

Answer is:

[false,false]

Is 1m equal to 1cm, and is 2m equal to 200cm?

[1m,2m]<==>[1cm,200cm];

Answer is:

[false,true]

Is 1m not equal to 1cm, and is 2m not equal to 200cm?

[1m,2m]<!=>[1cm,200cm];

Answer is:

[true,false]

Is 1m less than 1cm, and is 2m less than 199.99cm?

[1m,2m]<<=>[1cm,199.99cm];

Answer is:

[false,false]

Is 1m less than or equal to 1cm, and is 2m less than or equal to 199.99cm?

[1m,2m]<<=>[1cm,200.01cm];

Answer is:

[false,true]

Also note that it is not necessary for both sides of these to be the same size. For example, the following is a check to see which all numbers between 1m to 10m are greater than 3m.

((1..10)<>m)<>>3m;

And the answer is:

false

false

false

true

true

true

true

true

true

true

The following is a check to see which all numbers in the series 0.1m, 1.1m, upto 10m are greater than 30cm.

((0.1..10)<>m)<>>30cm

Numeric	Units	UNITSOF
0.1	m	0.1m
1.1	m	1.1m
2.1	m	2.1m
3.1	m	3.1m
4.1	m	4.1m
5.1	m	5.1m
6.1	m	6.1m
7.1	m	7.1m
8.1	m	8.1m
9.1	m	9.1m

The answer is:

false

true

true

true

true

true

true

true

true

true

Types of Supported Unit Conversions

z^3 unit conversions cover a large number of units, and is highly flexible in handling new units that are not known.

Basic Conversions

The command CONVERT() gives the list of basic units supported within z^3.

MassUnits:g,sg,lbm,u,ozm,

DistanceUnits:m,mi,Nmi,in,ft,yd,ang,Pica,

TimeUnits:yr,day,hr,mn,sec,year,s,min,hour,

PressureUnits:Pa,atm,mmHg,

ForceUnits:N,dyn,lbf,

EnergyUnits:J,e,c,cal,eV,HPh,Wh,flb,BTU,

PowerUnits:HP,W,

MagnetismUnits:T,ga,

LiquidUnits:tsp,tbs,oz,cup,pt,qt,gal,l,

Prefixes:Y,Z,E,P,T,G,M,k,h,e,d,c,m,u,n,p,FValue,a,z,y,

Others:rad,deg,F,C,K,dollar,euro,cent,rupee

Any custom user supplied conversions would also be listed.

Derived Conversions

The command SUPPORTEDUNITS() gives the list of derived and related units supported by z^3.

{ m.m−1: {

       radian: angle
       rad: angle
       }

m2.m−2: {

       steradian: solid angle
       sr: solid angle
       }

s−1: {

       hertz: frequency
       Hz: frequency
       becquerel: radioactivity (decays per unit time)
       Bq: radioactivity (decays per unit time)
       times: frequency
       }

kg.m.s−2: {

       newton: force, weight
       N: force, weight
       }

kg.m−1.s−2: {

       pascal: pressure, stress
       Pa: pressure, stress
       }

N/m2: {

       pascal: pressure, stress
       Pa: pressure, stress
       }

kg.m2.s−2: {

       joule: energy, work, heat
       J: energy, work, heat
       }

N.m: {

       joule: energy, work, heat
       J: energy, work, heat
       }

kg.m2.s−3: {

       watt: power, radiant flux
       W: power, radiant flux
       }

J/s: {

       watt: power, radiant flux
       W: power, radiant flux
       }

s.A: {

       coulomb: electric charge or quantity of electricity
       C: electric charge or quantity of electricity
       }

kg.m2.s−3.A−1: {

       volt: voltage (electrical potential difference), electromotive force
       V: voltage (electrical potential difference), electromotive force
       }

W/A: {

       volt: voltage (electrical potential difference), electromotive force
       V: voltage (electrical potential difference), electromotive force
       }

kg−1.m−2.s4.A2: {

       farad: electric capacitance
       F: electric capacitance
       }

C/V: {

       farad: electric capacitance
       F: electric capacitance
       }

kg.m2.s−3.A−2: {

       ohm: electric resistance, impedance, reactance
       Ω: electric resistance, impedance, reactance
       }

V/A: {

       ohm: electric resistance, impedance, reactance
       Ω: electric resistance, impedance, reactance
       }

kg−1.m−2.s3.A2: {

       siemens: electrical conductance
       S: electrical conductance
       }

A/V: {

       siemens: electrical conductance
       S: electrical conductance
       }

kg.m2.s−2.A−1: {

       weber: magnetic flux
       Wb: magnetic flux
       }

V.s: {

       weber: magnetic flux
       Wb: magnetic flux
       }

kg.s−2.A−1: {

       tesla: magnetic flux density
       T: magnetic flux density
       }

Wb/m2: {

       tesla: magnetic flux density
       T: magnetic flux density
       }

kg.m2.s−2.A−2: {

       henry: inductance
       H: inductance
       }

Wb/A: {

       henry: inductance
       H: inductance
       }

K: {

       degree Celsius: temperature relative to 273.15 K
       °C: temperature relative to 273.15 K
       }

cd: {

       lumen: luminous flux
       lm: luminous flux
       }

cd.sr: {

       lumen: luminous flux
       lm: luminous flux
       }

m−2.cd: {

       lux: illuminance
       lx: illuminance
       }

lm/m2: {

       lux: illuminance
       lx: illuminance
       }

m2.s−2: {

       gray: absorbed dose (of ionizing radiation)
       Gy: absorbed dose (of ionizing radiation)
       sievert: equivalent dose (of ionizing radiation)
       Sv: equivalent dose (of ionizing radiation)
       }

J/kg: {

       gray: absorbed dose (of ionizing radiation)
       Gy: absorbed dose (of ionizing radiation)
       sievert: equivalent dose (of ionizing radiation)
       Sv: equivalent dose (of ionizing radiation)
       }

mol.s−1: {

       katal: catalytic activity
       kat: catalytic activity
       }

6.283185307179586:rad.mn−1: {

       rpm: frequency
       }

}

{ angles: {

       rad: 1
       cycle: 0.15915494309189535
       deg: 57.29577951308232
       rotation: 0.15915494309189535
       revolution: 0.15915494309189535
       }

circle: {

       rad: 1
       cycle: 0.15915494309189535
       rotation: 0.15915494309189535
       revolution: 0.15915494309189535
       }

area: {

       m2: 1
       acre: 0.0002471053814671653
       acreUs: 0.00024710436922532533
       acreus: 0.00024710436922532533
       are: 0.01
       barn: NaN
       barony: 6.17763670801153e-8
       board: 129.16692500051667
       boilerHorsepowerEquivalentDirectRadiation: 0.07717136689166236
       boilerhorsepowerequivalentdirectradiation: 0.07717136689166236
       circularInch: 1973.5251599788835
       circularinch: 1973.5251599788835
       circularMil: 1973525159.9788833
       circularmil: 1973525159.9788833
       cord: 0.6727444010443576
       cuerda: 0.00025442731353539
       dunam: 0.001
       guntha: 0.009884353069091628
       hectare: 0.0001
       hide: 0.000002
       rood: 0.0009884215258686613
       section: 3.861021585424458e-7
       shed: 1e+52
       squareRoofing: 0.10763910416709721
       squareroofing: 0.10763910416709721
       squareChain: 0.0024710538146716535
       squarechain: 0.0024710538146716535
       squareChainUs: 0.0024710436922532534
       squarechainus: 0.0024710436922532534
       squareFoot: 10.763910416709722
       squarefoot: 10.763910416709722
       squareFootUs: 10.763867361111092
       squarefootus: 10.763867361111092
       squareInch: 1550.0031000062002
       squareinch: 1550.0031000062002
       squarekilometre: 0.000001
       squareLinkGuntersInternational: 24.710538146716537
       squarelinkguntersinternational: 24.710538146716537
       squarelinkGuntersUs: 24.710443028590973
       squarelinkguntersus: 24.710443028590973
       squareLinkramsdens: 10.763910416709722
       squarelinkramsdens: 10.763910416709722
       squareMetre: 1
       squaremetre: 1
       squareMil: 1550003100.0062
       squaremil: 1550003100.0062
       squareMile: 3.861021585424458e-7
       squaremile: 3.861021585424458e-7
       squareMileUs: 3.861006141829883e-7
       squaremileus: 3.861006141829883e-7
       squareRod: 0.039536861034746455
       squarerod: 0.039536861034746455
       squareYard: 1.1959900463010802
       squareyard: 1.1959900463010802
       stremma: 0.001
       township: 1.072501762656647e-8
       yardland: 0.000008333333333333334
       }

length: {

       Å: 10000000000
       angstrom: 10000000000
       ångström: 10000000000
       AU: 6.684587122268445e-12
       barleycorn: 118.20330969267138
       a0: NaN
       cablelengthimperial: 0.005396118248376848
       cablelengthinternational: 0.005399568034557236
       cablelengthus: 0.004556722076407116
       chain: 0.049709596537030665
       cubit: 2
       ell: 0.8748906386701663
       ftm: 0.5468066491688539
       fm: 999999999999999.9
       fermi: 44.994375703037115
       finger: 8.748906386701663
       footben: 3.2808427474518638
       footcape: 3.176034910975741
       footclarke: 3.2808693302666354
       footindian: 3.280845126281927
       footmetric: 3.1622776602367586
       footmetriclong: 3.3333333333333335
       footmetricshort: 3.3333333333333335
       foot: 3.280839895013123
       footsears: 3.280845599895564
       footus: 3.2808333290409095
       charriere: 3.3333333333333335
       fur: 0.004970969537898671
       furlong: 0.004970969537898671
       hand: 9.84251968503937
       in: 39.37007874015748
       lea: 0.00020712510356255177
       lightday: 3.860695546274908e-14
       lighthour: 9.265669311059779e-13
       lightminute: 5.5594015866358675e-11
       lightsecond: 3.3356409519815204e-9
       lightyear: 1.0570008340246154e-16
       ly: 1.0570008340246154e-16
       ln: 472.5897920604915
       lnk: 4.9709596537030665
       lnkengineers: 3.280839895013123
       m: 1
       mickey: 7874.0157480314965
       um: 1000000
       milethousand: 39370.07874015748
       milesweden: 0.0001
       milegeographical: 0.0005394343793181722
       mileinternational: 0.0006213711922373339
       miletactical: 0.0005468066491688539
       miletelegraph: 0.0005389912756716155
       mileus: 0.0006213699493769715
       nail: 17.497812773403325
       nm: 999999999.9999999
       NL: 0.00017998560115190784
       nl: 0.00017998560115190784
       NMadmiral: 0.0005396118248376848
       nmadmiral: 0.0005396118248376848
       NM: 0.0005399568034557236
       nmi: 0.0005399568034557236
       Nmus: 0.0005395931899022688
       nmus: 0.0005395931899022688
       pace: 1.3123359580052494
       palm: 13.123359580052492
       parsec: 3.240779289960431e-17
       pc: 3.240779289960431e-17
       pointamerican: 2845.354958031014
       pointeuropean: 2659.99999734
       pt: 2835.270768358378
       pttex: 2845.275619003937
       quarter: 4.374453193350831
       rd: 0.19883878151594686
       rope: 0.16404199475065617
       shaku: 3.3003300330033003
       span: 4.374453193350831
       spat: 1e-12
       stick: 19.68503937007874
       pm: 1000000000000
       twp: 56695.770495521036
       twip: 56695.770495521036
       xu: 9979044007584.074
       siegbahn: 9979044007584.074
       yd: 1.0936132983377078
       }

volume: {

       acft: 0.0008107131937899126
       acreFoot: 0.0008107131937899126
       acrefoot: 0.0008107131937899126
       acin: 0.009728558325478951
       acreInch: 0.009728558325478951
       acreinch: 0.009728558325478951
       barrelImperial: 6.110256897196883
       barrelimperial: 6.110256897196883
       bl: 6.289810770432105
       barrelPetroleum: 6.289810770432105
       barrelpetroleum: 6.289810770432105
       barrelUsDry: 8.648409373989104
       barrelusdry: 8.648409373989104
       flbl: 8.38641436057614
       barrelUsFluid: 8.38641436057614
       barrelusfluid: 8.38641436057614
       fbm: 423.77600065786305
       boardFoot: 423.77600065786305
       boardfoot: 423.77600065786305
       bkt: 54.992312074771945
       bucketImperial: 54.992312074771945
       bucketimperial: 54.992312074771945
       bushelImperial: 27.496156037385973
       bushelimperial: 27.496156037385973
       bushelUsDryHeaped: 22.702074606721396
       bushelusdryheaped: 22.702074606721396
       bu: 28.377593258401745
       bushel: 28.377593258401745
       bushelUsDryLevel: 28.377593258401745
       bushelusdrylevel: 28.377593258401745
       butt: 2.096603590144035
       pipe: 2.096603590144035
       coomb: 6.874039009346493
       cordFirewood: 0.2758958337616296
       cordfirewood: 0.2758958337616296
       cordFoot: 2.207166670093037
       cordfoot: 2.207166670093037
       cufm: 0.16349382741429902
       cubicFathom: 0.16349382741429902
       cubicfathom: 0.16349382741429902
       cuft: 35.31466672148859
       cubicFoot: 35.31466672148859
       cubicfoot: 35.31466672148859
       cuin: 61023.74409473229
       cubicInch: 61023.74409473229
       cubicinch: 61023.74409473229
       m3: 1
       cubicMetre: 1
       cubicmetre: 1
       cumi: 2.3991275857892774e-10
       cubicMile: 2.3991275857892774e-10
       cubicmile: 2.3991275857892774e-10
       cuyd: 1.3079506193143922
       cubicYard: 1.3079506193143922
       cubicyard: 1.3079506193143922
       cupBreakfast: 3519.5079727854045
       cupbreakfast: 3519.5079727854045
       cupCanadian: 4399.384965981755
       cupcanadian: 4399.384965981755
       c: 4000
       cup: 4000
       cupUs: 4226.752837730374
       cupus: 4226.752837730374
       cupUsFood: 4166.666666666667
       cupusfood: 4166.666666666667
       dashImperial: 2702982.1230991934
       dashimperial: 2702982.1230991934
       dash: 3246146.179376928
       dashUs: 3246146.179376928
       dashus: 3246146.179376928
       dessertSpoonImperial: 84468.19134732537
       dessertspoonimperial: 84468.19134732537
       dropImperial: 10136182.961631099
       dropimperial: 10136182.961631099
       dropImperialAlt: 12839165.164612733
       dropimperialalt: 12839165.164612733
       dropMedical: 12043839.576056847
       dropmedical: 12043839.576056847
       dropMedicalA: 12004801.920768308
       dropmedicala: 12004801.920768308
       drop: 20000000
       gtt: 20000000
       dropUs: 12173048.172664467
       dropus: 12173048.172664467
       dropUsA: 15419194.352040531
       dropusa: 15419194.352040531
       dropUsB: 19476877.07626125
       dropusb: 19476877.07626125
       fifth: 1320.860261790742
       firkin: 24.44102758878753
       fluidDrachm: 281560.63782283233
       fluiddrachm: 281560.63782283233
       fldr: 270512.18161474395
       fldram: 270512.18161474395
       fluidDram: 270512.18161474395
       fluiddram: 270512.18161474395
       fls: 844681.9134732537
       fluidScruple: 844681.9134732537
       fluidscruple: 844681.9134732537
       beerGallon: 216.39625565507905
       beergallon: 216.39625565507905
       gallonBeer: 216.39625565507905
       gallonbeer: 216.39625565507905
       gallonImperial: 219.96924829908778
       gallonimperial: 219.96924829908778
       gallonUsDry: 227.02074606721396
       gallonusdry: 227.02074606721396
       gallonUsFluid: 264.1720523581484
       gallonusfluid: 264.1720523581484
       gillimperial: 7039.015945570809
       noggin: 7039.015945570809
       nog: 7039.015945570809
       gillUs: 8453.505675460749
       gillus: 8453.505675460749
       gi: 8453.505675460749
       hogsheadImperial: 3.0551284485984413
       hogsheadimperial: 3.0551284485984413
       hhd: 4.19320718028807
       hogshead: 4.19320718028807
       jigger: 22542.83137962128
       kilderkin: 12.220513794393765
       λ: 999999999.9999999
       lamda: 999999999.9999999
       last: 0.34370195046732466
       L: 1000
       liter: 1000
       load: 0.7062933344297718
       minim: 16893638.269379456
       minimImperial: 16893638.269379456
       minimimperial: 16893638.269379456
       minimUs: 16230730.896884637
       minimus: 16230730.896884637
       min: 16230730.896884637
       flozImperial: 35195.07972785404
       flozimperial: 35195.07972785404
       usFloz: 33814.022701842994
       usfloz: 33814.022701842994
       floz: 33814.022701842994
       flozUs: 33814.022701842994
       flozus: 33814.022701842994
       flozUsnutrition: 33333.333333333336
       flozusnutrition: 33333.333333333336
       pkImperial: 109.98462414954389
       pkimperial: 109.98462414954389
       peckImperial: 109.98462414954389
       peckimperial: 109.98462414954389
       pk: 113.51037303360698
       peckUs: 113.51037303360698
       peckus: 113.51037303360698
       perch: 1.426855221070246
       per: 1.426855221070246
       pinchImperial: 1351491.0615496074
       pinchimperial: 1351491.0615496074
       pinch: 1623073.089688464
       pintImperial: 1759.7539863927022
       pintimperial: 1759.7539863927022
       pintUsDry: 1816.1659685377117
       pintusdry: 1816.1659685377117
       pint: 2113.376418865187
       pintUsFluid: 2113.376418865187
       pintusfluid: 2113.376418865187
       pony: 45085.36360245733
       pottle: 439.93849659817556
       quartern: 439.93849659817556
       qtImperial: 879.8769931963511
       qtimperial: 879.8769931963511
       qtUsDry: 908.0829842688559
       qtusdry: 908.0829842688559
       qtUsFluid: 1056.6882094325936
       qtusfluid: 1056.6882094325936
       quart: 1056.6882094325936
       qt: 1056.6882094325936
       quarter: 3.4370195046732466
       pail: 3.4370195046732466
       registerTon: 0.3531466672148859
       registerton: 0.3531466672148859
       sackImperial: 9.165385345795325
       sackimperial: 9.165385345795325
       bag: 9.165385345795325
       sackUs: 9.459197752800582
       sackus: 9.459197752800582
       sack: 9.459197752800582
       seam: 3.547199157300218
       shot: 22727.272727272728
       strikeImperial: 13.748078018692986
       strikeimperial: 13.748078018692986
       strikeUs: 14.188796629200873
       strikeus: 14.188796629200873
       strike: 14.188796629200873
       tbspAustralianMetric: 49999.99999999999
       tbspaustralianmetric: 49999.99999999999
       tbspCanadian: 70390.15945570808
       tbspcanadian: 70390.15945570808
       tbspImperial: 56312.12756456647
       tbspimperial: 56312.12756456647
       tbsp: 66666.66666666667
       tbspUs: 67628.04540368599
       tbspus: 67628.04540368599
       tbspFood: 66666.66666666667
       tbspfood: 66666.66666666667
       tspCanadian: 211170.4783968529
       tspcanadian: 211170.4783968529
       tspImperial: 168936.38269379456
       tspimperial: 168936.38269379456
       tsp: 199999.99999999997
       tspUs: 202884.136211058
       tspus: 202884.136211058
       tspFood: 199999.99999999997
       tspfood: 199999.99999999997
       timberFoot: 35.31466672148859
       timberfoot: 35.31466672148859
       tonDisplacement: 1.0089904777568168
       tondisplacement: 1.0089904777568168
       ton: 0.8828666680372148
       tonFreight: 0.8828666680372148
       tonfreight: 0.8828666680372148
       tonWater: 0.9820055727637849
       tonwater: 0.9820055727637849
       tun: 1.0483017950720175
       wey: 0.7094398314600436
       }

angle: {

       angularMil: 1018.5913289357351
       angularmil: 1018.5913289357351
       arcMinute: 3437.7492368196695
       arcminute: 3437.7492368196695
       MOA: 3437.7492368196695
       arcSecond: 206264.7982101166
       arcsecond: 206264.7982101166
       centesimalminuteOfArc: 6366.182836771071
       centesimalminuteofarc: 6366.182836771071
       centesimalsecondOfArc: 636619.9048125918
       centesimalsecondofarc: 636619.9048125918
       °: 57.29577793714916
       degree: 57.29577793714916
       degreeOfArc: 57.29577793714916
       degreeofarc: 57.29577793714916
       grad: 63.66197832271442
       gradian: 63.66197832271442
       gon: 63.66197832271442
       octant: 1.2732398096251836
       quardrant: 0.6366199048125918
       rad: 1
       sextant: 0.9549292492919199
       sign: 1.9098584985838398
       }

solid angle: {

       squareDegree: 3282.778543759438
       squaredegree: 3282.778543759438
       sqdeg: 3282.778543759438
       deg2: 3282.778543759438
       steradian: 1
       sr: 1
       }

mass: {

       u: 6.022141290116741e+26
       AMU: 6.022141290116741e+26
       atomicMassUnit: 6.022141290116741e+26
       atomicmassunit: 6.022141290116741e+26
       me: 1.0977692011412001e+30
       massOfElectron: 1.0977692011412001e+30
       massofelectron: 1.0977692011412001e+30
       bag: 0.023453432147327404
       bagofcoffee: 0.016666666666666666
       bagofportlandcement: 0.023453432147327404
       barge: 0.000048991613818861684
       kt: 0.0048733763227731645
       ct: 0.005
       carat: 0.005
       clove: 0.27557782773109696
       crith: 0.011119153965813049
       dalton: 6.022141290116741e+26
       drT: 0.25720597254902383
       drt: 0.25720597254902383
       dramTroy: 0.25720597254902383
       dramtroy: 0.25720597254902383
       drAv: 0.5643833911932866
       drav: 0.5643833911932866
       dramAvoirdupois: 0.5643833911932866
       dramavoirdupois: 0.5643833911932866
       eV: 5.609588860666922e+35
       ev: 5.609588860666922e+35
       electronVolt: 5.609588860666922e+35
       electronvolt: 5.609588860666922e+35
       γ: 1
       gamma: 1
       gr: 0.01543235835294143
       grain: 0.01543235835294143
       gv: 1
       grave: 1
       longCwt: 0.01968413055222121
       longcwt: 0.01968413055222121
       cwt: 0.01968413055222121
       shCwt: 0.022046226218487758
       shcwt: 0.022046226218487758
       cental: 0.022046226218487758
       kg: 1
       kip: 0.002204622621848776
       mark: 0.004018843321078497
       mite: 0.3086471670588286
       mitemetric: 0.02
       ozT: 0.03215074656862798
       ozt: 0.03215074656862798
       ounceTroy: 0.03215074656862798
       ouncetroy: 0.03215074656862798
       ozAv: 0.035273961949580414
       ozav: 0.035273961949580414
       ounceAvoirdupois: 0.035273961949580414
       ounceavoirdupois: 0.035273961949580414
       oz: 0.03571428571428571
       ounce: 0.03571428571428571
       ounceFood: 0.03571428571428571
       ouncefood: 0.03571428571428571
       dwt: 0.6430149313725596
       Pwt: 0.6430149313725596
       pwt: 0.6430149313725596
       pennyweight: 0.6430149313725596
       point: 0.5
       lbAv: 2.2046226218487757
       lbav: 2.2046226218487757
       poundAvoidupois: 2.2046226218487757
       poundavoidupois: 2.2046226218487757
       poundMetric: 0.002
       poundmetric: 0.002
       pound: 0.002
       lb: 0.002
       poundTroy: 2.6792288807189983
       poundtroy: 2.6792288807189983
       quarterImperial: 0.07873652220888484
       quarterimperial: 0.07873652220888484
       quarterInformal: 0.004409245243697552
       quarterinformal: 0.004409245243697552
       quarterLong: 0.003936826110444242
       quarterlong: 0.003936826110444242
       q: 0.01
       quintal: 0.01
       sAp: 0.7716179176470715
       sap: 0.7716179176470715
       scruple: 0.7716179176470715
       sheet: 0.001543235835294143
       slug: 0.06852176556196105
       geepound: 0.06852176556196105
       hyl: 0.06852176556196105
       stone: 0.1574730444177697
       AT: 0.03429355281207133
       tonLongAssay: 0.03067484662576687
       tonlongassay: 0.03067484662576687
       tonShortAssay: 0.03429355281207133
       tonshortassay: 0.03429355281207133
       longTn: 0.0009842065276110606
       longtn: 0.0009842065276110606
       ton: 0.0009842065276110606
       shTn: 0.001102311310924388
       shtn: 0.001102311310924388
       shortTon: 0.001102311310924388
       shortton: 0.001102311310924388
       t: 0.001
       tonne: 0.001
       wey: 0.008748502467653872
       }

density: {

       g/mL: 0.001
       g/ml: 0.001
       g.mL-1: 0.001
       g.ml-1: 0.001
       kg/m3: 1
       kg.m-3: 1
       kg/L: 0.001
       kg/l: 0.001
       kg.L-1: 0.001
       kg.l-1: 0.001
       oz/ft3: 0.9988473690911163
       oz.ft-3: 0.9988473690911163
       oz/in3: 0.0005780366721308782
       oz.in-3: 0.0005780366721308782
       oz/gal: 0.16035860569078172
       oz.gal-1: 0.16035860569078172
       oz/galUs: 0.13352647123776576
       oz/galus: 0.13352647123776576
       oz.gal-1Us: 0.13352647123776576
       oz.gal-1us: 0.13352647123776576
       lb/ft3: 0.06242796059157827
       lb.ft-3: 0.06242796059157827
       lb/in3: 0.0000361272920003488
       lb.in-3: 0.0000361272920003488
       lb/gal: 0.00834540445319611
       lb.gal-1Imperial: 0.0000361272920003488
       lb.gal-1imperial: 0.0000361272920003488
       lb.gal-1Us: 0.00834540445319611
       lb.gal-1us: 0.00834540445319611
       slug/ft3: 0.0019403203319541004
       slug.ft-3: 0.0019403203319541004
       }

time: {

       au: 41341374575750990
       atomicunitoftime: 41341374575750990
       callippicCycle: 4.1723410504953406e-10
       callippiccycle: 4.1723410504953406e-10
       c: 3.168873850681143e-10
       century: 3.168873850681143e-10
       d: 0.000011574074074074073
       day: 0.000011574074074074073
       sd: 0.000011605761564270966
       siderealDay: 0.000011605761564270966
       siderealday: 0.000011605761564270966
       dec: 3.168873850681143e-9
       decade: 3.168873850681143e-9
       fn: 8.267195767195768e-7
       fortnight: 8.267195767195768e-7
       helek: 0.30303030303030304
       hipparchicCycle: 1.0423806974444161e-10
       hipparchiccycle: 1.0423806974444161e-10
       h: 0.0002777777777777778
       hour: 0.0002777777777777778
       j: 60.24096385542168
       jiffy: 60.24096385542168
       ja: 100
       jiffyAlternative: 100
       jiffyalternative: 100
       ke: 0.0011111111111111111
       quarterHour: 0.0011111111111111111
       quarterhour: 0.0011111111111111111
       quarterOfAnHour: 0.0011111111111111111
       quarterofanhour: 0.0011111111111111111
       keTraditional: 0.0011574074074074073
       ketraditional: 0.0011574074074074073
       lustre: 6.341958396752917e-9
       lustrum: 6.341958396752917e-9
       metonicCycle: 1.6677340164371864e-9
       metoniccycle: 1.6677340164371864e-9
       Enneadecaeteris: 1.6677340164371864e-9
       enneadecaeteris: 1.6677340164371864e-9
       millenium: 3.168873850681143e-11
       md: 0.011574074074074073
       milliday: 0.011574074074074073
       min: 0.016666666666666666
       minute: 0.016666666666666666
       moment: 0.011111111111111112
       month: 3.8580246913580245e-7
       monthFull: 3.8580246913580245e-7
       monthfull: 3.8580246913580245e-7
       monthGregorian: 3.802715138608967e-7
       monthgregorian: 3.802715138608967e-7
       monthHollow: 3.9910600255427844e-7
       monthhollow: 3.9910600255427844e-7
       mo: 3.920031360250882e-7
       monthSynodic: 3.920031360250882e-7
       monthsynodic: 3.920031360250882e-7
       octateris: 3.961010976753618e-9
       planckTime: 7.400763889678921e+42
       plancktime: 7.400763889678921e+42
       s: 1
       sec: 1
       shake: 100000000
       sigma: 1000000
       sothicCycle: 2.1704169735636267e-15
       sothiccycle: 2.1704169735636267e-15
       svedberg: 100000000000
       wk: 0.0000016534391534391535
       week: 0.0000016534391534391535
       a: 3.1709791983764586e-8
       Y: 3.1709791983764586e-8
       annum: 3.1709791983764586e-8
       year: 3.1709791983764586e-8
       yearGregorian: 3.168873850681143e-8
       yeargregorian: 3.168873850681143e-8
       yearJulian: 3.168808781402895e-8
       yearjulian: 3.168808781402895e-8
       yearLeap: 3.1623153207852664e-8
       yearleap: 3.1623153207852664e-8
       yearMeanTropical: 3.1688765619590626e-8
       yearmeantropical: 3.1688765619590626e-8
       yearSidereal: 3.1687535787224804e-8
       yearsidereal: 3.1687535787224804e-8
       }

speed: {

       fph: 11820.33096926714
       footPerHour: 11820.33096926714
       footperhour: 11820.33096926714
       fpm: 196.85039370078738
       footPerMinute: 196.85039370078738
       footperminute: 196.85039370078738
       fps: 3.280839895013123
       footPerSecond: 3.280839895013123
       footpersecond: 3.280839895013123
       furlongPerFortnight: 6012.885613870525
       furlongperfortnight: 6012.885613870525
       iph: 141843.97163120567
       inchPerHour: 141843.97163120567
       inchperhour: 141843.97163120567
       ipm: 2364.066193853428
       inchPerMinute: 2364.066193853428
       inchperminute: 2364.066193853428
       ips: 39.37007874015748
       inchPerSecond: 39.37007874015748
       inchpersecond: 39.37007874015748
       km/h: 3.7037037037037033
       kmph: 3.7037037037037033
       kn: 1.9426038273180604
       knot: 1.9455252918287937
       knotAdmiralty: 1.9426038273180604
       knotadmiralty: 1.9426038273180604
       M: 0.002913752913752914
       machNumber: 0.002913752913752914
       machnumber: 0.002913752913752914
       mach: 0.002913752913752914
       m/s: 1
       mps: 0.0006213711922373339
       meterPerSecond: 1
       meterpersecond: 1
       mph: 2.2369362920544025
       milePerHour: 2.2369362920544025
       mileperhour: 2.2369362920544025
       mpm: 0.03728227153424004
       milePerMinute: 0.03728227153424004
       mileperminute: 0.03728227153424004
       milePerSecond: 0.0006213711922373339
       milepersecond: 0.0006213711922373339
       speedOfLight: 3.3356409519815204e-9
       speedoflight: 3.3356409519815204e-9
       speedOfSound: 0.002913752913752914
       speedofsound: 0.002913752913752914
       }

flow: {

       CFM: 2118.8800032893155
       cfm: 2118.8800032893155
       ft3/s: 35.31466672148859
       in3/min: 3661424.6903707054
       in3/s: 61023.74409473229
       m3/s: 1
       GPD: 22824465.328374747
       gpd: 22824465.328374747
       GPH: 951019.3887908136
       gph: 951019.3887908136
       GPM: 15850.323141488903
       gpm: 15850.323141488903
       LPM: 62500
       lpm: 62500
       }

acceleration: {

       fph/s: 11820.33096926714
       fpm/s: 196.85039370078738
       fps2: 3.280839895013123
       Gal: 100
       gal: 100
       ipm/s: 2364.066193853428
       ips2: 39.37007874015748
       kn/s: 1.9455252918287937
       m/s2: 1
       mph/s: 2.2369362920544025
       mpm/s: 0.03728227153424004
       mps2: 0.0006213711922373339
       ɡ0: 0.10197162129779283
       }

force: {

       atomicUnitOfForce: 12137804.779883545
       atomicunitofforce: 12137804.779883545
       dyn: 99999.99999999999
       dyne: 99999.99999999999
       kgf: 0.10197162129779283
       kp: 0.10197162129779283
       Gf: 0.10197162129779283
       gf: 101.97162129779282
       kip: 0.0002248089430997105
       kipf: 0.0002248089430997105
       klbf: 0.0002248089430997105
       mGf: 101.97162129779282
       mgf: 101.97162129779282
       tnf: 100.36113531237075
       longTonForce: 100.36113531237075
       longtonforce: 100.36113531237075
       N: 1
       ozf: 3.596943089595368
       ounceForce: 3.596943089595368
       ounceforce: 3.596943089595368
       lbf: 0.2248089430997105
       poundForce: 0.2248089430997105
       poundforce: 0.2248089430997105
       pdl: 7.233013851209894
       poundal: 7.233013851209894
       stnf: 0.00011240447154985525
       shortTonForce: 0.00011240447154985525
       shorttonforce: 0.00011240447154985525
       sn: 0.001
       sthene: 0.001
       }

pressure: {

       atm: 0.000009869232667160129
       atmosphere: 0.000009869232667160129
       at: 0.000010197162129779282
       bar: 0.009523809523809525
       bareye: 10
       cmHg: 0.0007500637554192106
       cmhg: 0.0007500637554192106
       cmOfMercury: 0.0007500637554192106
       cmofmercury: 0.0007500637554192106
       centimetreOfMercury: 0.0007500637554192106
       centimetreofmercury: 0.0007500637554192106
       cmH2O: 0.010197442889221099
       cmh2o: 0.010197442889221099
       cmOfWater: 0.010197442889221099
       cmofwater: 0.010197442889221099
       CentimetreOfWater: 0.010197442889221099
       centimetreofwater: 0.010197442889221099
       ftHg: 0.000024608321648481936
       fthg: 0.000024608321648481936
       footOfMercury: 0.000024608321648481936
       footofmercury: 0.000024608321648481936
       ftH2O: 0.000334562292153176
       fth2o: 0.000334562292153176
       footOfWater: 0.000334562292153176
       footofwater: 0.000334562292153176
       inHg: 0.0002952998016471232
       inhg: 0.0002952998016471232
       inchOfMercury: 0.0002952998016471232
       inchofmercury: 0.0002952998016471232
       inH2O: 0.00401474213311279
       inh2o: 0.00401474213311279
       inchOfWater: 0.00401474213311279
       inchofwater: 0.00401474213311279
       kgf/mm2: 1.0197162129779283e-7
       ksi: 1.450377438972831e-7
       ltpsf: 0.000009323854568370791
       longTonPerSquareFoot: 0.000009323854568370791
       longtonpersquarefoot: 0.000009323854568370791
       umHg: 7.500615050434135
       umhg: 7.500615050434135
       micrometreOfMercury: 7.500615050434135
       micrometreofmercury: 7.500615050434135
       mmHg: 0.0075006150504341364
       mmhg: 0.0075006150504341364
       millimetreOfMercury: 0.0075006150504341364
       millimetreofmercury: 0.0075006150504341364
       mmH2O: 0.10197442889221098
       mmh2o: 0.10197442889221098
       mmOfWater: 0.10197442889221098
       mmofwater: 0.10197442889221098
       millimeterOfWater: 0.10197442889221098
       millimeterofwater: 0.10197442889221098
       Pa: 1
       pa: 1
       pascal: 1
       pz: 0.001
       pieze: 0.001
       psf: 0.02088543378837124
       poundPerSqft: 0.02088543378837124
       poundpersqft: 0.02088543378837124
       psi: 0.00014503774389728312
       poundPerSqin: 0.00014503774389728312
       poundpersqin: 0.00014503774389728312
       pdl/sqFt: 0.6719689496587742
       pdl/sqft: 0.6719689496587742
       poundalPerSqft: 0.6719689496587742
       poundalpersqft: 0.6719689496587742
       stnpsf: 0.000010442717112286298
       shortTonPerSquareFoot: 0.000010442717112286298
       shorttonpersquarefoot: 0.000010442717112286298
       torr: 0.0075006150504341364
       }

torque: {

       ft·lbf: 0.7375621492772654
       ft·pdl: 23.730360404231938
       in·lbf: 8.850745791327185
       m·kgf: 0.10197162129779283
       N·m: 1
       n·m: 1
       }

energy: {

       boe: 1.6339869281045752e-10
       BTUISO: 0.000948316737790422
       BTUIT: 0.0009478171203133172
       BTUmean: 0.0009470862890317938
       btumean: 0.0009470862890317938
       BTUth: 0.0009484516526770049
       btuth: 0.0009484516526770049
       BTU39degF: 0.0009436900167033133
       btu39degf: 0.0009436900167033133
       BTU59degF: 0.0009480434279733486
       btu59degf: 0.0009480434279733486
       BTU60degF: 0.0009481548905829255
       btu60degf: 0.0009481548905829255
       BTU63degF: 0.0009482268158543524
       btu63degf: 0.0009482268158543524
       calIT: 0.23884589662749595
       calit: 0.23884589662749595
       calmean: 0.23866234528713468
       calth: 0.2390057361376673
       Cal: 0.00023884589662749592
       cal: 0.00023884589662749592
       cal3point98degC: 0.2378404090855036
       cal3point98degc: 0.2378404090855036
       cal15degC: 0.2389200812328276
       cal15degc: 0.2389200812328276
       cal20degC: 0.2391257562352041
       cal20degc: 0.2391257562352041
       CHUIT: 0.0005265650668407317
       ccAtm: 9.869232667160128
       ccatm: 9.869232667160128
       scc: 9.869232667160128
       cuFtAtm: 0.0003485286624375878
       cuftatm: 0.0003485286624375878
       Scf: 0.0003485286624375878
       scf: 0.0003485286624375878
       cuftOfNaturalGas: 9.478171203133172e-7
       cuftofnaturalgas: 9.478171203133172e-7
       cuYdAtm: 0.000012908468979169922
       cuydatm: 0.000012908468979169922
       Scy: 0.000012908468979169922
       scy: 0.000012908468979169922
       eV: 6241509343260179000
       ev: 6241509343260179000
       erg: 10000000
       ftLbf: 0.7375621492772654
       ftlbf: 0.7375621492772654
       ftPdl: 23.730360404231938
       ftpdl: 23.730360404231938
       impGalAtm: 0.0021709276910840147
       impgalatm: 0.0021709276910840147
       USGalAtm: 0.002607175448883774
       usgalatm: 0.002607175448883774
       Eh: 229371265835792200
       eh: 229371265835792200
       hpH: 3.7250613599861886e-7
       hph: 3.7250613599861886e-7
       inLbf: 8.850745791327185
       inlbf: 8.850745791327185
       J: 1
       kcal: 0.00023884589662749592
       kWH: 2.7777777777777776e-7
       kwh: 2.7777777777777776e-7
       BOTU: 2.7777777777777776e-7
       lAtm: 0.009869232667160128
       latm: 0.009869232667160128
       Sl: 0.009869232667160128
       sl: 0.009869232667160128
       quad: 9.478171203133173e-19
       Ry: 458742531671584400
       ry: 458742531671584400
       rydberg: 458742531671584400
       thermEc: 9.478171203133172e-9
       thermec: 9.478171203133172e-9
       thermUs: 9.480434279733487e-9
       thermus: 9.480434279733487e-9
       th: 2.388458966274959e-7
       thermie: 2.388458966274959e-7
       TCE: 3.414367659109533e-11
       toe: 2.3884589662749594e-11
       tTNT: 2.390057361376673e-10
       ttnt: 2.390057361376673e-10
       }

power: {

       atmCcm: 592.1539600296077
       atmccm: 592.1539600296077
       atmCcs: 9.869232667160128
       atmccs: 9.869232667160128
       atmCfh: 1.254703181097798
       atmcfh: 1.254703181097798
       atmCfm: 0.02091171974625527
       atmcfm: 0.02091171974625527
       atmCfs: 0.0003485286624375878
       atmcfs: 0.0003485286624375878
       BTUIT/h: 3.4121424501230075
       btuit/h: 3.4121424501230075
       BTUIT/min: 0.05686902789903518
       btuit/min: 0.05686902789903518
       BTUIT/s: 0.0009478171203133172
       btuit/s: 0.0009478171203133172
       calIT/s: 0.23884589662749595
       calit/s: 0.23884589662749595
       erg/s: 10000000
       ft·lbf/h: 2655.2237145464574
       ft·lbf/min: 44.253728956635925
       ft·lbf/s: 0.7375621492772654
       hpBoiler: 0.00010194199500484225
       hpboiler: 0.00010194199500484225
       hpEuropeanElectrical: 0.001358695652173913
       hpeuropeanelectrical: 0.001358695652173913
       hpElectrical: 0.0013404825737265416
       hpelectrical: 0.0013404825737265416
       hpMechanical: 0.0013410220895950279
       hpmechanical: 0.0013410220895950279
       hp: 0.0013596216173039043
       PS: 0.0013596216173039043
       L·atm/min: 0.5921539600296077
       l·atm/min: 0.5921539600296077
       L·atm/s: 0.009869232667160128
       l·atm/s: 0.009869232667160128
       lusec: 7501.875468867218
       p: 0.0010197162129779282
       poncelet: 0.0010197162129779282
       sqFtEDR: 0.014217256772628402
       sqftedr: 0.014217256772628402
       tonOfAirConditioning: 0.00028538812785388126
       tonofairconditioning: 0.00028538812785388126
       tonOfRefrigerationImperial: 0.0002538795976008378
       tonofrefrigerationimperial: 0.0002538795976008378
       tonOfRefrigeration: 0.00028434512332474514
       tonofrefrigeration: 0.00028434512332474514
       W: 1
       }

dynamic viscosity: {

       Pa·s: 1
       pa·s: 1
       P: 10
       poise: 10
       lb/(ft·h): 2419.088153749502
       lb/(ft·s): 0.6719689496587742
       lbf·s/ft2: 0.02088543378837124
       lbf·s/in2: 0.00014503774389728312
       }

kinematic viscosity: {

       ft2/s: 10.763910416709722
       m2/s: 1
       St: 10000
       st: 10000
       stokes: 10000
       }

electric current: {

       A: 1
       ampere: 1
       abamp: 0.1
       esu/s: 2997924536.8431435
       }

electric charge: {

       abC: 0.1
       abc: 0.1
       emu: 0.1
       au: 6241509744511525000
       atomicUnitOfCharge: 6241509744511525000
       atomicunitofcharge: 6241509744511525000
       C: 1
       coulomb: 1
       F: 0.000010364268992774003
       faraday: 0.000010364268992774003
       mA·h: 0.2777777777777778
       ma·h: 0.2777777777777778
       statC: 2997924536.8431435
       statc: 2997924536.8431435
       Fr: 2997924536.8431435
       fr: 2997924536.8431435
       Esu: 2997924536.8431435
       esu: 2997924536.8431435
       }

electric dipole: {

       ea0: 1.1794743889644761e+29
       C·m: 1
       c·m: 1
       D: 2.997924581780902e+29
       debye: 2.997924581780902e+29
       }

electric voltage: {

       abV: 100000000
       abv: 100000000
       statV: 0.0033356409519815205
       statv: 0.0033356409519815205
       V: 1
       volt: 1
       }

magnetic flux: {

       Mx: 100000000
       mx: 100000000
       maxwell: 100000000
       Wb: 1
       wb: 1
       weber: 1
       }

magnetic field: {

       G: 10000
       gauss: 10000
       T: 1
       tesla: 1
       }

information count: {

       bit: 1
       b: 1
       Sh: 1
       sh: 1
       nibble: 0.25
       byte: 0.125
       B: 0.125
       kBDecimal: 0.000125
       kbdecimal: 0.000125
       kilobyteDecimal: 0.000125
       kilobytedecimal: 0.000125
       kB: 0.0001220703125
       kb: 0.0001220703125
       KiB: 0.0001220703125
       kib: 0.0001220703125
       kilobyte: 0.0001220703125
       KB: 0.0001220703125
       }

luminous intensity: {

       cd: 1
       candela: 1
       cp: 1
       candlePower: 1
       candlepower: 1
       cpold: 1.019367991845056
       candlePowerPre1948: 1.019367991845056
       candlepowerpre1948: 1.019367991845056
       }

luminance: {

       cd/ft2: 0.09290303999749462
       cd/in2: 0.0006451600000025807
       cd/m2: 1
       fL: 0.2918635079631734
       fl: 0.2918635079631734
       footLambert: 0.2918635079631734
       footlambert: 0.2918635079631734
       L: 0.00031415926536272057
       lambert: 0.00031415926536272057
       sb: 0.009615384615384616
       stilb: 0.009615384615384616
       }

illuminance: {

       fc: 0.09290303999749462
       footCandle: 0.09290303999749462
       footcandle: 0.09290303999749462
       lm/in2: 0.0006451600000025807
       lx: 1
       lux: 1
       ph: 0.009615384615384616
       phot: 0.009615384615384616
       }

radioactivity: {

       Bq: 1
       bq: 1
       becquerel: 1
       Ci: 2.7027027027027027e-11
       ci: 2.7027027027027027e-11
       curie: 2.7027027027027027e-11
       rd: 0.000001
       rutherford: 0.000001
       }

}

Behavior on Unit Conversion Failures

In general, if a conversion fails, the original value with units are returned. This behavior can be changed so that a unit conversion if not possible, would return a null value. To do this, change the global variable UNITSFAILTONULL to true.

The following will give 1m as the result.

1m<>eor

1 m

UNITSFAILTONULL=true

1m<>eor

will now give null as the result.

UNITSFAILTONULL=false

1m<>eor

1 m

will be shown as the result.

Interesting Techniques

Long Variable Names can be used in the expressions, including units as given below.

##weight of zone=3m; 

++(##weight of zone);

weightofzone+4;

Please note that ##weight of zone is the same as weightofzone.

Constants

Several useful constants are already defined in z^3, and can be accessed by prefixing % to the name of the constant. While doing this, you can simply give a few of the letters to indicate the constant, rather than the full name. These names can be space separated also.

For example:

%planck;

6.62607004081e-34 J s.

%boltzmann;

1.380648813e-23 J K-1.

%planck length;

1.61619997e-35 m.

To get a listing of all the CONSTANTS currently supported (along with units the numbers are represented in), simply give the command to z^3:

CONSTANTS()

speed of light in vacuum	299792458 m·s−1
speed of sound in dry air	343.2 m·s−1
newtonian constant of gravitation	6.6740831e−11 m3·kg−1·s−2
planck constant	6.62607004081e−34 J·s
reduced planck constant	1.05457180013e−34 J·s
magnetic constant vacuum permeability	1.256637061e−6 N·A−2
electric constant vacuum permittivity	8.854187817e−12 F·m−1
characteristic impedance of vacuum	376.730313461 Ω
coulomb's constant	8.987551787e9 N·m2·C−2
elementary charge	1.60217656535e−19 C
bohr magneton	9.2740096820e−24 J·T−1
conductance quantum	7.748091734625e−5 S
inverse conductance quantum	12906.403721742 Ω
josephson constant	4.8359787011e14 Hz·V−1
magnetic flux quantum	2.06783375846e−15 Wb
nuclear magneton	5.0507835311e−27 J·T−1
von klitzing constant	25812.807443484 Ω
bohr radius	5.291772109217e−11 m
classical electron radius	2.817940326727e−15 m
electron mass	9.1093829140e−31 kg
fermi coupling constant	1.1663645e−5 GeV−2
fine-structure constant	7.297352569824e−3
hartree energy	4.3597443419e−18 J
proton mass	1.67262177774e−27 kg
quantum of circulation	3.636947552024e−4 m2 s−1
rydberg constant	10973731.56853955 m−1
thomson cross section	6.65245873413e−29 m2
weak mixing angle	0.222321
efimov factor	22.7
atomic mass constant	1.66053892173e−27 kg
avogadro's number	6.0221412927e23 mol−1
boltzmann constant	1.380648813e−23 J·K−1
faraday constant	96485.336521C·mol−1
first radiation constant	3.7417715317e−16 W·m2
first radiation constant for spectral radiance	1.19104286953e−16 W·m2·sr−1
loschmidt constant	2.686780524e25 m−3
gas constant	8.314462175 J·K−1·mol−1
molar planck constant	3.990312717628e−10 J·s·mol−1
molar volume of an ideal gas at T=273.15K and p=100kPa	2.271095321e−2 m3·mol−1
molar volume of an ideal gas at T=273.15K and p=101.325 kPa	2.241396820e−2 m3·mol−1
sackur-tetrode constant at T=1 K and p=100kPa	−1.151707823
sackur-tetrode constant at T=1 K and p=101.325 kPa	−1.164870823
second radiation constant	1.438777013e−2 m·K
stefan–boltzmann constant	5.67037321e−8 W·m−2·K−4
wien displacement law constant	2.897772126e−3 m·K
conventional value of josephson constant	4.835979e14 Hz·V−1
conventional value of von klitzing constant	25812.807 Ω
molar mass constant	1e−3 kg·mol−1
molar mass constant of carbon-12	1.2e−2 kg·mol−1
standard acceleration of gravity (gee, free-fall on earth)	9.80665 m·s−2
gee	9.80665 m·s−2
standard atmosphere	101325 Pa
planck length	1.61619997e−35 m
planck mass	2.1765113e−8 kg
planck time	5.3910632e−44 s
planck charge	1.87554595641e−18 C
planck temperature	1.41683385e32 K

MORE

/* THESE ARE BEING DOCUMENTED NOW */

(1..100)<>l<>ul 1Pa<>atm

E:=(m<>kg)<*>(SPEEDOFLIGHT()<^>2); b=E(2g); ConvertToUnitOfNature(b,"energy")

CONSTANT("G") CONSTANT("G")<*>1kg<*>110kg</>(6000m<^>2) // did not work.

(CONSTANT("G")<*>1kg<*>110kg)</>((6000m)<^>2) // how to bracket the units to be inside and ignore < etc? // ## can be used to name variables with spaces in them. // the actual variable is named by removing the spaces. // otherwise it goes into code as it is.

//%G is gravitational constant GF:=%G*m1*m2/r^2; GF(1,2,300)

v:=u+%g*t; // this uses %g as default g value v(1,2)

PRINTCONVERSIONS()

      CONVERT()

A¹=34; A=[23,4,5,5]; /* no array indexing on subscript yet. Will decide on that later. */ A¹=[23,4,5,5] A¹[2]

a=%gravit; b=30<*>a

a=%gravit; b=(1..10)<*>a

E:=m<>kg<*>%c<^>2; E(1000kg) E(1000kg<>lbm) // - will gave same result as 1000kg E(1000lbm) //lbm is used for units of lb mass.

// %G<*>1kg<*>110kg(6000m<^>2) // %G<*>1kg<*>110kg((6000m)<^>2) // -did not work. Said 7.34149141e-9Nm3UNITPOWERUNITSOF %G<*>1kg<*>110kg<*>((6000m)<^>2)

%G<*>1kg<*>110kg</>((6000m)<^>2)

// make this work. 1..100 @> x.txt; // send output to a <@ x.txt; // read input from a;

1.3J<>GeV 1.3J<>eV

1J<>l.atm; // 0.0098692latm 1J<>(l.atm-1) // this should fail. and will keep original units. maybe safer. 1m2<>in2 1m²<>in²

10m2<>are 1m2<>are

100m2<>acre

E:=m<>kg<*>%c<^>2; b=E(1000kg)<>J

   c=b<>eV;

[b,c]

1..100.$("[SIN(x),COS(x),TAN(x)]") 1..100.$([SIN,COS,TAN]) worked. 1..100.$("[x,x^2,x^3,x^4,x^3+x^4,SIN(x)]") works 1..100.$("[SIN(x),COS(x),TAN(x)]") 1..100.$([SIN,COS,TAN]) x=SERIESOF("1/x",9,10) //this is to from in parameter sequence. x=SERIESOF("1/x",19,10) SERIESOF("1/x",10,5) x=SERIESOF "1/LOG(x,2)" 100 1 x=SERIESOF "1/log2x" 100 91 //removed: 1..10.$_([+,-]) 1..10.$_([SUM,MINUS]) //removed: 1..10.$_|+| EXPOF(5) [SIN,COS]@[1..100] 1..10.$_("+") 1..10.$_("+") 1..10@["+"] 1..10@"+"

(1..100)<>m<+>10cm

MAGICSQUARE(3).$$(SUM) MAGICSQUARE(3).$$$(SUM) MAGICSQUARE(3).$_(SUM)

a=1m<>mm<+>400km 1m<>eor // should give nothing as there is no such conversion. (((1..100)<>m)<^>2)<>are

(1..1000)<>$ (((1..100)<>m)<^>2)<>km2 // why chinese headers here?

(1..100)m<>cm

F=%G<*>100kg<*>10g</>((100km)<^>2);

1.3J<>GeV //check this

velocity=3<>(m/sec); time=1hr; velocity<*>time;

1(g.m)<>(mg.cm)

a=LAZYRANGE(1,100) a(1..100) // generate numbers in the range at that interval, without having to generate the array ahead of time. Useful in things like INTEGRALS etc. a() a=LAZYOBJECT(1,100,1000) // can even take a(0.1); a.islazyrange()

1(kg.m2s-2)<>(N.m) 1(kg.m2s-2)<>J 1(kg.m2s-2)<>(N) // also should work as we want to get rid of the /s here in this case. 1(kg.m2s-2)<>(N.m2) // should fail. 1(kg.m2s-2)<>(J/s) // should fail. 1(kg.m2s-3)<>(J/s) 1(kg.m2.s)<>(J/s) // should this fail? it works now.

12(g.m-1/s)<>(g.cm) // should fail. 12(g.m)<>(g.mm) // should not fail. 12(g.m)<>(g.cm) // should not fail.

12(g.m)<>(g.s) // should fail. original should be returned. 12(g.m)<>(g.mm) 12(g.m)<>(g.s) 12(g.m-1)<>(g.mm-1) 12(g.m-1/s)<>(g.cm-1) // converts, but this is ok, since /s on left sometimes we want to get rid off for some reason for using it on another calculation. Say N/s but you only want to use the N on it. 1(kg.m2/s2)<>e // how to make this conversion?

1(kg.m2/s2)<>J<>e

1.3(kg.m2/s2)<>Jo // would fail and original will be kept.

(((1..100)<>m)<^>2)<>are (1..100)<>are [1cm2,2m2]<>are %pi*34; %e; %avo;

q=1(mol/s); heat=%avo<*>q;

1Pa<>atm 1atm<>psi 1atm<>hPa

a=1<>(kg/m.s-2)<>Pa<>torr 1J<>BTU 1ly<>m 10ly<>m<>km

1atm<>inHg<>mmHg

1atm<+>1bar (1atm<+>1bar)<>atm 1km<>m<>lightyear

1lightyear<>km

1lightyear<>pc

1m<>ly

1km<>ly //seemed off. this is possibly correct. (1km<+>1ly)<>km

1Å<>km

1Å<>m

(1..100)<>AU<>m

1degree<>arcminute

1Tsec<>sec

1(m/s)<>(km/hr) 1(km/s)<>(km/hr)

1(cal/mn)<>(J/sec) // d

1(kg/m3)<>(slug.ft-3)

2(rad/sec)<>rpm // did not convert. not sure why.

(1..100)<>USD<>EUR

SUPPORTEDUNITS()

1nibble<>bit 102400000000bit<>MB 1kB<>MB // seems wrong. 1kB<>Mb 1(kb)<>(bit) Pi<>(rad/sec)<>rpm 1(rad/sec)<>rpm 1(rad/mn)<>rpm (1(rad/mn)<>rpm)*2*Pi // should give 1. 1(rotation/mn)<>rpm 1(cycle/mn)<>(rad/mn)

1(cycle/mn)<>rpm

60rad<>deg 60rad<>deg<>rotation

1MB<>kB 1B<>kB 1MB<>B 1kB<>B

a=1(kg/m/s-2/t3) a=1(kg/m/s-2/t3) a=1(kg/m/s-2/t3) a=1(kg/m/s-2/t3) a=1<>(kg/m.s-2) // this worked though.

1(kg/m3)<>(slug/ft^3) // will not work due to ^. 1(kg/m3)<>(slug/ft3) //works 1(kg/m3)<>(slug.ft-3) //works

1(s-1)<>Hz 1(mn-1)<>Hz

velocity=3<>(m/s); time=1hr; velocity<*>time;

(((1..100)<>m)<^>2)<>acre

((1..100)<>m)<^>2