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