Rules for Entering Units
In Calcumber, spaces are significant when working with units. Use spaces to separate numbers, units, and operators, but not within a unit expression.
Use space between number and unit:
| 5 m # unit meter | 5 m |
| 5m # multiplier milli | 0.005 |
End unit expressions with a space:
| 5 m^2 # square metres | 5 m2 |
| 5 m ^2 # square the value 5 m | 25 m2 |
| 1 m+1 m # space missing | |
| 1 m + 1 m # space between 'm' and '+' | 2 m |
| (1 m)^2 # bracket after unit is fine | 1 m2 |
Don't use space within unit expressions:
| You defined in some preceeding calculation: | |
| Mass: m = 5 kg | 5 kg |
| Now you calculate torque: | |
| correct: T = 18 N*m # unit Newton metre (=J) | 18 J |
| wrong: T = 18 N * m # multiply by variable m | 90 N*kg |
Unit Conversion
For unit conversion, use the keyword to or in.
Use to base or in base to convert to base units.
| 50 mph to km/h | 80.4672 km/h |
| 3 gal in L | 11.356235 L |
| Miles per gallon to L/100 km: | |
| 1 / 23 mi/gal | 0.043478261 gal/mi |
| ans to cl/km # = L/100 km | 10.226721 cl/km |
| Weight of US Letter Paper: | |
| 8.5 inch * 11 inch * 80 g/m2 to g | 4.8257968 g |
| To base units: | |
| 1 mph to base | 0.44704 m/s |
| 10 N to base | 10 kg*m/s2 |
Partial conversion: If the requested target unit does not match the dimension of the input quantity, Calcumber performs a partial conversion and preserves the remaining dimensions. This can reveal interesting physical relationships:
| 1 W to s # Power is energy per unit time | 1 J/s |
| 1 L to cm # Volume is length cubed | 1000 cm3 |
| 1 Pa to J # Pressure is energy per unit volume | 1 J/m3 |
| 1 mm to L # Rainfall depth and volume | 1 L/m2 |
Using Undefined Units
Units do not need to be predefined. Undefined units can still be used in calculations and may either cancel out or remain in the result.
| Using undefined unit 'person': | |
| water_consumption = 150 L/person/day * 8000 person to m3/h | 50 m3/h |
| Using undefined unit 'EUR': | |
| energy_bill = 0.29 EUR/kWh * 7600 kWh/year | 2204 EUR/year |
Multiplier Prefixes
Many units support multiplier prefixes. Example using Joule:
| 1 aJ to J # atto | 1e-18 J |
| 1 fJ to J # femto | 1e-15 J |
| 1 pJ to J # pico | 1e-12 J |
| 1 nJ to J # nano | 1e-9 J |
| 1 uJ to J # micro | 1e-6 J |
| 1 µJ to J # micro | 1e-6 J |
| 1 mJ to J # milli | 0.001 J |
| 1 cJ to J # centi | 0.01 J |
| 1 dJ to J # deci | 0.1 J |
| 1 J | 1 J |
| 1 DJ to J # deka | 10 J |
| 1 hJ to J # hecto | 100 J |
| 1 kJ to J # kilo | 1000 J |
| 1 MJ to J # mega | 1e6 J |
| 1 GJ to J # giga | 1e9 J |
| 1 TJ to J # tera | 1e12 J |
| 1 PJ to J # peta | 1e15 J |
| 1 EJ to J # exa | 1e18 J |
List of Units
SI Units
Base Units:
| 1 m # length, meter | 1 m |
| 1 s # time, second | 1 s |
| 1 kg # mass, kilogram | 1 kg |
| 1 A # electrical current, Ampère | 1 A |
| 1 K # temperature, Kelvin | 1 K |
| 1 mol # amount of substance, mole | 1 mol |
| 1 cd # luminous intensity, candela | 1 cd |
Derived Units:
| 1 g to kg # gram | 0.001 kg |
| 1 Hz to 1/s # Hertz | 1 1/s |
| 1 N to kg*m/s^2 # Newton | 1 kg*m/s2 |
| 1 Pa to N/m2 # Pascal | 1 N/m2 |
| 1 J to N*m # Joule | 1 N*m |
| 1 W to J/s # Watt | 1 J/s |
| 1 C to A*s # Coulomb | 1 A*s |
| 1 V to J/C # Volt | 1 J/C |
| 1 Ohm to V/A # Ohm | 1 V/A |
| 1 S to 1/Ohm # Siemens | 1 1/Ohm |
| 1 F to C/V # Farad | 1 C/V |
| 1 Wb to V*s # Weber | 1 V*s |
| 1 T to V*s/m2 # Tesla | 1 V*s/m2 |
| 1 H to V*s/A # Henry | 1 V*s/A |
| 1 lm to cd*sr # lumen | 1 cd*sr |
| 1 lx to lm/m2 # lux | 1 lm/m2 |
| 1 Bq to 1/s # Becquerel | 1 1/s |
| 1 Gy to J/kg # Gray | 1 J/kg |
| 1 Sv to J/kg # Sievert | 1 J/kg |
| 1 kat to mol/s # katal | 1 mol/s |
Angular and Scalar Units
Angular units:
| 1 rad to 1 # radian | 1 |
| 180 deg to 1 # degree | 3.14159 |
| 180° to 1 # ° unit works without space | 3.14159 |
| 1 deg to arcmin | 60 arcmin |
| 1 arcmin to arcsec | 60 arcsec |
| 1 sr to 1 # steradian | 1 |
Scalar units:
| 1 % to 1 # percent | 0.01 |
| 50% to 1 # % unit works without space | 0.5 |
| 1 ppm to 1 # parts per million | 1e-6 |
| Calculating a percent value: | |
| 4.8 / 6.7 in % | 71.6418 % |
| Thermal Expansion: | |
| CTE = 45 ppm/K | 45 ppm/K |
| l = 1.5 m | 1.5 m |
| ΔT = 70 K | 70 K |
| Δl = CTE * l * ΔT to mm | 4.725 mm |
| l + Δl | 1.50473 m |
Length
| 1 inch to m # inch | 0.0254 m |
| 1 in # 'in' is keyword (alias for to) | |
| 1 mil to inch # thousandth of inch | 0.001 inch |
| 1 ft to inch # foot | 12 inch |
| 1 mi to ft # mile | 5280 ft |
| 1 yd to ft # yard | 3 ft |
| 1 au to m # astronomical unit | 1.4959787e11 m |
| 1 dioptre in 1/m # dioptre | 1 1/m |
Area
| 1 are to m2 # are | 100 m2 |
| 1 ac to ft2 # acre | 43560 ft2 |
| 1 ha to m2 # hectare | 10000 m2 |
Volume
| 1 L to dm3 # litre | 1 dm3 |
| 1 l to dm3 # litre | 1 dm3 |
| 1 gal to L # US gallon | 3.7854118 L |
| 1 gal to qt # US quart | 4 qt |
| 1 qt to pt # US pint | 2 pt |
| 1 gal to floz # US fluid ounce | 128 floz |
| 1 floz to tbsp # tablespoon | 2 tbsp |
| 1 floz to tsp # teaspoon | 6 tsp |
| 1 cup to L # Approx. metric cup | 0.24 L |
Time
| 1 min to s | 60 s |
| 1 h to min | 60 min |
| 1 d to h | 24 h |
| 1 week to d | 7 d |
| 1 month to d | 30.4375 d |
| 1 year to d | 365.25 d |
| 1 year to month | 12 month |
Aliases:
hour,
hours,
day,
days,
weeks,
a,
years,
months
Speed
SI-unit is m/s.
| 1 mph to km/h # miles per hour | 1.609344 km/h |
| 1 fps to m/s # foot per second | 0.3048 m/s |
| 1 knot to km/h # nautical mile per hour | 1.852 km/h |
Mass
Si-unit is kg.
| 1 t to kg # ton | 1000 kg |
| 1 lb to kg # pound (avoirdupois) | 0.45359237 kg |
| 1 lb to oz # ounce | 16 oz |
| 1 st to lb # stone | 14 lb |
| 1 ton_us to lb # US ton | 2000 lb |
| 1 ton_uk to lb # UK long ton | 2240 lb |
| 1 Da to kg # Dalton | 1.6605391e-27 kg |
Energy and Power
Energy: SI unit is J or W*s.
| 1 eV to J # electronvolt | 1.6021764e-19 J |
| 1 Wh to J # Watt hour | 3600 J |
| 1 BTU to J # British thermal unit | 1055.0559 J |
| 1 cal to J # calorie | 4.184 J |
| 1 Cal to J # Used on food labels = 1 kcal | 4184 J |
Power: SI unit is W or J/s.
| 1 TR to Btu/h # Ton of refrigeration | 12000 Btu/h |
| 1 hp to W # Horse power | 745.7 W |
Temperature and Temperature Conversion
The following temperature units are defined in Calcumber:
| K | Kelvin. Base unit for all temperatures. |
| °C or degC | Degree Celsius |
| °F or degF | Degree Fahrenheit |
| °Ra or degRa | Degree Rankine |
By default, all temperature values are interpreted as temperature
differences. Therefore, converting °C to Kelvin will not add 273.15 K.
This behavior prevents interpretation problems in many calculations as
shown in the example below:
| Expression | Result |
|---|---|
| Mass: m = 100 kg | 100 kg |
| Temp. increase: ΔT = 40 °C | 40 °C |
| Spec. heat: cp = 4182 J/(kg*K) | 4182 J/(kg*K) |
| Energy needed: | |
| m * ΔT * cp to kWh | 4.6466667 kWh |
Heating up 100 kg of water by 40°C needs 4.6 kWh. If Calcumber would convert 40°C to 313 K, the result would be 36.4 kWh, which would be the value for heating it up from 0 K to 313 K.
For converting actual temperature values between the scales, use the defined conversion functions as below:
| Expression | Result |
|---|---|
| Conversion of temperature differences: | |
| 10 °C to K | 10 K |
| 10 °F to K | 5.5555556 K |
| Conversion of temperature values: | |
| to_K(10 °C) | 283.15 K |
| to_K(10 °F) | 260.92778 K |
| to_degF(0 °C) | 32 °F |
| to_degC(0 °F) | -17.777778 °C |
| to_degRa(1000 °C) | 2291.67 °Ra |
Force and Pressure
Force: Si-unit is N.
| 1 lbf to N # pound-force | 4.4482216 N |
Pressure: Si-unit is Pa.
| 1 bar to Pa | 100000 Pa |
| 1 psi to bar # pounds per square inch | 0.068947573 bar |
| 1 atm to bar # standard atmosphere | 1.01325 bar |