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Units are objects that have 2 separate parts: the value and the unit per se. The value is usually a real number, but units may be attached to other numerical objects as well, for example complex numbers and vectors or matrices can have associated units. The unit part is entered using the underscore _
, which acts as both a separator and an operator.
The unit is an algebraic expression combining one or more unit symbols, and may be optionally surrounded by square brackets. The brackets are optional for stack input, but mandatory when units are used within a symbolic expression (to separate the unit from other algebraic operations). The _
key will always add the brackets regardless of whether the user is typing an algebraic expression or not, the use of the brackets is encouraged.
Examples of valid unit objects are:
1_m
3_m/s^2
3_[m/s^2]
[1 2 3]_kg
'3_[m]+2_[ft]'
in all cases above, the underscore is being used as a separator, but can be used as an operator as well:
_[m]
[1 2 3] _[kg]
in the first case, the operator _[]
will apply the unit to some value previously left on the stack. In the second case, the value (a vector) is separated with a space, therefore it will be compiled as a separate object, put on the stack, and then the underscore operator will apply the unit.
Exponents within a unit expression can be integer numbers, real numbers or fractional exponents. The use of fractional exponents is always preferred over real numbers because they can be simplified in an exact way.
3_[m^(2/3)]
is always preferred to 3_[m^0.666667]
Unit objects can be operated upon normally, and the system will perform all the necessary unit conversions in the background. Unit consistency is strictly enforced for addition and subtraction, therefore if one variable uses units in an algebraic expression, all variables should have proper units attached.
Results of an addition or subtraction between consistent units will produce a result with the units of the first argument (argument in level 2 of the stack at the time of the operation, or the left argument in an algebraic expression).
This is a list of the units available in the Units
menu on newRPL:
Length |
Unit | Unit name | Definition | Description |
1_m | metre | 1_m | Base SI unit of length |
1_cm | centimetre | 1_cm = 0.01_m | SI length |
1_mm | millimetre | 1_mm = 0.001_m | SI length |
1_yd | yard | 1_yd = 3_ft | US customary length |
1_ft | foot | 1_ft = 12_in | US customary length |
1_in | inch | 1_in = 0.0254_m | US customary length |
1_Mpc | megaparsec | 1_Mpc = 1000000_pc | Astronomical length |
1_pc | parsec | 1_pc = (648000/π)_au | Astronomical length |
1_lyr | light year | 1_lyr = 365.25_d*c | Astronomical length |
1_au | astronomical unit | 1_au = 149597870700_m | SI astronomical length |
1_km | kilometre | 1_km = 1000_m | SI length |
1_mi | mile | 1_mi = 5280_ft | US customary length |
1_nmi | nautical mile | 1_nmi = 1852_m | non-SI length |
1_miUS | surveying mile | 1_miUS = 5280_ftUS | US surveying length |
1_chain | surveying chain | 1_chain = 66_ftUS | US surveying length |
1_rd | rod | 1_rd =16.5_ft | US customary length |
1_rdUS | surveying rod | 1_rdUS =16.5_ftUS | US surveying length |
1_fath | surveying fathom | 1_fath =6_ftUS | US surveying length |
1_ftUS | surveying foot | 1_ftUS = 1200/3937_m | US surveying length |
1_mil | thousandth of inch | 1_mil = 0.001_in | US customary length |
1_µ | micron or micrometre | 1_µ = 1_µm | SI length |
1_Å | Ångström | 1_Å = 0.1_nm | non-SI length |
1_fermi | fermi or femtometre | 1_fermi = 1_fm | SI length |
Area |
Unit | Unit name | Definition | Description |
1_m^2 | square metre | 1_m^2 | Base SI unit of area |
1_cm^2 | square centimetre | 1_cm^2 = 0.0001_m^2 | SI area |
1_b | barn | 1_b = 1E-28_m^2 | non-SI area |
1_yd^2 | square yard | 1_yd^2 = 9_ft^2 | US customary area |
1_ft^2 | square foot | 1_ft^2 = 144_in^2 | US customary area |
1_in^2 | square inch | 1_in^2 = 6.4516_cm^2 | US customary area |
1_km^2 | square kilometre | 1_km^2 = 1E6_m^2 | SI area |
1_ha | hectare | 1_ha = 1_hm^2 | SI area (deprecated) |
1_a | are | 1_a = 100_m^2 | non-SI area |
1_mi^2 | square mile | 1_mi^2 = 9_ft^2 | US customary area |
1_miUS^2 | survey square mile | 1_miUS^2 = 9_ftUS^2 | US surveying area |
1_acre | acre | 1_acre = 4840_yd^2 | US customary area |
Volume |
Unit | Unit name | Definition | Description |
1_m^3 | cubic metre | 1_m^3 | Base SI unit of volume |
1_cm^3 | cubic centimetre | 1_cm^3 = 1E-6_m^3 | SI volume |
1_ml | millilitre | 1_ml = 1_cm^3 | SI volume |
1_l | litre | 1_l = 0.001_m^3 | SI volume |
1_st | stere | 1_st = 1_m^3 | non-SI volume |
1_yd^3 | cubic yard | 1_yd^3 = 27_ft^3 | US customary volume |
1_ft^3 | cubic foot | 1_ft^3 = 1728_in^3 | US customary volume |
1_in^3 | cubic inch | 1_in^3 = 16.387064_cm^3 | US customary volume |
1_gal | gallon | 1_gal = 231_in^3 | US customary volume |
1_qt | quart | 1_qt = 1/4_gal | US customary volume |
1_pt | pint | 1_pt = 1/8_gal | US customary volume |
1_cu | cup | 1_cu = 1/16_gal | US customary volume |
1_ozfl | fluid ounce | 1_ozfl = 1/128_gal | US customary volume |
1_tbsp | table spoon | 1_tbsp = 1/2_ozfl | US customary volume |
1_tsp | tea spoon | 1_tsp = 1/6_ozfl | US customary volume |
1_fbm | board foot | 1_fbm = 144_in^3 | US customary volume |
1_galUK | gallon (UK) | 1_galUK = 0.00454609_m^3 | Imperial volume |
1_qtUK | quart (UK) | 1_qtUK = 1/4_galUK | Imperial volume |
1_ptUK | pint (UK) | 1_ptUK = 1/8_galUK | Imperial volume |
1_ozUK | ounce (UK) | 1_ozUK = 1/160_galUK | US customary volume |
1_galC | gallon (Canada) | 1_galC = 1_galUK | Canadian volume |
1_qtC | quart (Canada) | 1_qtC = 1_qtUK | Canadian volume |
1_ptC | pint (Canada) | 1_ptC = 1_ptUK | Canadian volume |
1_ozC | ounce (Canada) | 1_ozC = 1_ozUK | Canadian volume |
1_bbl | oil barrel | 1_bbl = 42_gal | oil industry volume |
1_bu | bushel (US) | 1_bu = 2150.42_in^3 | US customary volume |
1_pk | peck (US) | 1_pk = 1/4_bu | US customary volume |
1_buUK | bushel (UK) | 1_buUK = 8_galUK | Imperial volume |
1_pkUK | peck (UK) | 1_pkUK = 1/4_buUK | Imperial volume |
1_buC | bushel (Canada) | 1_buC = 8_galC | Canadian volume |
1_pkC | peck (Canada) | 1_pkC = 1/4_buC | Canadian volume |
Time |
Unit | Unit name | Definition | Description |
1_yr | tropical year | 1_yr = 31556925.9747_sper | 1952 Ephemeris Time |
1_d | day | 1_d = 86400_s | SI time |
1_h | hour | 1_h = 3600_s | SI time |
1_min | minute | 1_min = 60_s | SI time |
1_s | second | 1_s | Base SI unit of time |
1_Hz | Hertz | 1_Hz = 1_1/s | SI frequency |
Speed |
Unit | Unit name | Definition | Description |
1_m/s | metres per second | 1_m/s | Base SI unit of speed |
1_cm/s | centimetres per second | 1_cm/s = 0.01_m/s | SI speed |
1_ft/s | feet per second | 1_ft/s = 12_in/s | US customary speed |
1_kph | kilometres per hour | 1_kph = 1_km/h | SI speed |
1_mph | miles per hour | 1_mph = 1_mi/h | SI speed |
1_knot | nautical knot | 1_knot = 1_nmi/h | non-SI speed |
1_c | speed of light | 1_c = 299792458_m/s | non-SI speed |
1_r/s | radians per second | 1_r/s | Base SI angular speed |
1_rpm | revolutions per minute | 1_rpm = 1_tr/min | non-SI speed |
1_tr/s | turns per second | 1_tr/s = 2π_r/s | non-SI speed |
Acceleration |
Unit | Unit name | Definition | Description |
1_m/s^2 | metre per second squared | 1_m/s^2 | SI acceleration |
1_cm/s^2 | centimetre per second squared | 1_cm/s^2 = 0.01_m/s^2 | SI acceleration |
1_ft/s^2 | foot per second squared | 1_ft/s^2 | US customary acceleration |
1_ga | acceleration of gravity | 1_ga = 9.80665_m/s^2 | non-SI acceleration |
1_r/s^2 | radian per second squared | 1_r/s^2 | SI angular acceleration |
Mass |
Unit | Unit name | Definition | Description |
1_kg | kilogram | 1_kg | Base SI unit of mass |
1_g | kilogram | 1_g = 0.001_kg | SI mass |
1_lb | pound | 1_lb = 7000_grain | US customary mass |
1_oz | ounce | 1_oz = 1/16_lb | US customary mass |
1_slug | slug | 1_slug = 1_lb*s^2/ft*ga | US customary mass |
1_lbt | troy pound | 1_lbt = 5760_grain | US customary mass |
1_ton | tonne | 1_ton = 2000_lb | US customary mass |
1_tonUK | tonne (UK) | 1_tonUK = 2240_lb | Imperial mass |
1_t | Metric tonne | 1_t = 1000_kg | non-SI mass |
1_ozt | troy ounce | 1_ozt = 480_grain | Imperial mass |
1_ct | Metric carat | 1_ct = 200_mg | Metric System mass |
1_grain | grain | 1_grain = 64.79891_mg | Imperial mass |
1_u | unified atomic mass | 1_u = 1.660539040E-27_kg | non-SI mass |
1_mol | mole | 1_mol | Base SI amount of substance |
1_gmol | gram mole | 1_gmol = 1_mol | non-SI amount of substance |
1_lbmol | pound mole | 1_lbmol = 453.59237_mol | US customary substance |
Force |
Unit | Unit name | Definition | Description |
1_N | Newton | 1_N = 1_kg*m/s^2 | SI force |
1_dyn | dyne | 1_dyn = 1_g*cm/s^2 | non-SI force |
1_gf | gram-force | 1_gf = 1_g*ga | non-SI force |
1_kip | kip | 1_kip = 1000_lbf | US customary force |
1_lbf | pound-force | 1_lbf = 1_lb*ga | US customary force |
1_pdl | poundal | 1_pdl = = 1_lb*ft/s^2 | US customary force |
Energy |
Unit | Unit name | Definition | Description |
1_J | Joule | 1_J = 1_N*m | SI energy |
1_kW*h | kilowatt-hour | 1_kW*h = 3.6_MJ | non-SI energy |
1_erg | erg | 1_erg = 1_dyn*cm | non-SI energy |
1_kcal | kilo calorie | 1_kcal = 1000_cal | non-SI energy |
1_cal | calorie | 1_cal = 4.184_J | non-SI energy |
1_Btu | british thermal unit | 1_Btu = =1055.056_J | Imperial energy |
1_ft*lbf | foot-pound | 1_ft*lbf = 1_lb*ft*ga | US customary energy |
1_therm | therm | 1_therm = 100000_Btu | Imperial energy |
1_MeV | mega electronvolt | 1_MeV = 1E6_eV | non-SI energy |
1_eV | electronvolt | 1_eV = 1.6021766208E-19_J | non-SI energy |
Power |
Unit | Unit name | Definition | Description |
1_W | Watt | 1_W = 1_J/s | SI power |
1_kW | kilowatt | 1_kW = 1000_W | SI power |
1_MW | megawatt | 1_MW = 1000000_W | SI power |
1_hp | mechanical horsepower | 1_hp = 550_ft*lbf/s | Imperial power |
1_lbf*ft/s | pound-foot per second | 1_ft*lbf/s | Imperial power |
Pressure |
Unit | Unit name | Definition | Description |
1_Pa | Pascal | 1_Pa = 1_N/m^2 | SI pressure |
1_atm | atmospheric pressure | 1_atm = 101325_Pa | non-SI pressure |
1_bar | bar | 1_bar = 100000_Pa | non-SI pressure |
1_psi | pound per square inch | 1_psi = 1_lbf/in^2 | US customary pressure |
1_Torr | Torricelli | 1_Torr = 1/760_atm | non-SI pressure |
1_mmHg | millimetres of mercury (at 0°C) | 1_mmHg = 13595.1_kg/m^3*mm*ga | non-SI pressure |
1_inHg | inches of mercury (at 0°C) | 1_inHg = 13595.1_kg/m^3*in*ga | non-SI pressure |
1_inH2O | inches of water (at 4°C) | 1_inH2O = 999.972_kg/m^3*in*ga | non-SI pressure |
Temperature |
Unit | Unit name | Definition | Description |
1_°C | celsius (or degree celsius) | 1_°C Zero: 0_°C → 273.15_K | Base SI temperature (rel. scale) |
1_Δ°C | celsius temperature change | 1_Δ°C = 1_ΔK | Change of temperature |
1_°F | farenheit (or degree farenheit) | 1_°F Zero: 0_°F → 459.67_°R | US cust. temp. (rel. scale) |
1_Δ°F | farenheit temperature change | 1_Δ°F = 1_Δ°R | Change of temperature |
1_K | kelvin | 1_K | Base SI temperature (abs. scale) |
1_ΔK | kelvin temperature change | 1_ΔK | Base change of temperature |
1_°R | rankine | 1_°R = 5/9_K | Imperial temperature (abs. scale) |
1_Δ°R | rankine temperature change | 1_Δ°R = 5/9_ΔK | Change of temperature |
Electricity and Magnetism |
Unit | Unit name | Definition | Description |
1_V | volt | 1_V = 1_J/C | SI potential difference |
1_A | ampere | 1_A | Base SI electric current |
1_C | coulomb | 1_C = 1_A*s | SI electrical charge |
1_Ω | ohm | 1_Ω = 1_V/A | SI electrical resistance |
1_F | farad | 1_F = 1_C/V | SI electrical capacity |
1_A*h | ampere-hour | 1_A*h = 3600_C | non-SI electrical charge |
1_Fdy | faraday | 1_Fdy = 96485.33289_C | non-SI electrical charge |
1_H | henry | 1_H = 1_Wb/A | SI inductance |
1_mho | mho (Siemens) | 1_mho = 1_S | non-SI conductance |
1_S | siemens | 1_S = 1_1/Ω | SI conductance |
1_T | tesla | 1_T = 1_Wb/m^2 | SI magnetic flux density |
1_Wb | weber | 1_Wb = 1_kg*m^2/A/s^2 | SI magnetic flux |
Angles |
Unit | Unit name | Definition | Description |
1_° | degree | 1_° = 2π/360_r | non-SI plane angle |
1_r | radian | 1_r | Base SI plane angle |
1_grad | grad (gon) | 1_grad = 2π/400_r | non-SI plane angle |
1_tr | full turn (one revolution) | 1_tr = 2π_r | non-SI plane angle |
1_arcmin | arc minute | 1_arcmin = 1/60_° | non-SI plane angle |
1_arcs | arc second | 1_arcmin = 1/3600_° | non-SI plane angle |
1_sr | steradian | 1_sr | Base SI solid angle |
Light |
Unit | Unit name | Definition | Description |
1_fc | foot-candle | 1_fc = 1_lm/ft^2 | non-SI illuminance |
1_flam | footlambert | 1_flam = 1/π_cd/ft^2 | non-SI illuminance |
1_lx | lux | 1_lx = 1_lm/m^2 | SI illuminance |
1_ph | phot | 1_ph = 1_lm/cm^2 | non-SI illuminance |
1_sb | stilb | 1_sb = 1_cd/cm^2 | non-SI illuminance |
1_lm | lumen | 1_lm = 1_cd*sr | SI luminous flux |
1_cd | candela | 1_cd | Base SI luminous intensity |
1_lam | lambert | 1_lam = 10000/π_cd/m^2 | non-SI illuminance |
Radiation |
Unit | Unit name | Definition | Description |
1_Gy | gray | 1_Gy = 1_J/kg | SI radiation |
1_rad | rad | 1_rad = 0.01_Gy | non-SI radiation |
1_rem | roentgen equivalent man | 1_rem = 1_erg/g | SI radiation |
1_Bq | becquerel | 1_Bq = 1_1/s | SI radiation |
1_Ci | curie | 1_Ci = 3.7E10_Bq | non-SI radiation |
1_R | rontgen | 1_R = 2.58E-4_C/kg | non-SI radiation |
Viscosity |
Unit | Unit name | Definition | Description |
1_P | poise | 1_P = 0.01_Pa*s | non-SI dynamic viscosity |
1_St | stokes | 1_St = 0.0001_m^2/s | non-SI kinematic viscosity |
1_m^2/s | square metre per second | 1_m^2/s | SI kinematic viscosity |
1_kg/(m*s) | kilogram per metre per second | 1_kg/(m*s) = 1_Pa*s | SI dynamic viscosity |