In math—particularly in physics—it is common practice to check the units of the answer to ensure they are compatible. Metres cannot be added to seconds or kilograms, if looking for an answer in seconds, all other units must cancel, etc.

It should be possible for the computer to track this using objects and overloading of +-*/. Has this been done before? If not, I'll just make it.

Example behaviour:

import dimanal as da

second = da.Unit('s')
metre = da.Unit('m')
kilogram = da.Unit('kg')

hour = 3600*second
kilo = 1000

v0 = 5*metre/second
# 5 m/s
# 5
# 18

v1 = 30*metre/second

v = v0 + v1  # Units match. No error.
    v = v0 + 80*kilogram  # Unit mismatch. Will cause exception.
except da.UnitMismatch:

t = 50*kilo*metre/v
assert(type(t/second) == float)  # unit check

2 Answers 2


The is pint which is a Python package to define, operate and manipulate physical quantities.

  • Python 2.6+, 3
  • BSD licence
  • Usable with numpy without patching numpy
  • Handles conversions between compatible units and errors on incompatibles.
  • Pure python & standalone module


In [1]: import pint

In [2]: ureg = pint.UnitRegistry()

In [4]: a = 0.3 * ureg.meter

In [5]: b = 1 * ureg.inch

In [6]: a+b
Out[6]: <Quantity(0.32539999999999997, 'meter')>

In [7]: _.to(ureg.inch)
Out[7]: <Quantity(12.811023622047243, 'inch')>

In [8]: _
Out[8]: <Quantity(12.811023622047243, 'inch')>

In [9]: _ * (12 * ureg.pound_force)
Out[9]: <Quantity(153.7322834645669, 'force_pound * inch')>

In [10]: _.to(ureg.joule)
Out[10]: <Quantity(17.369415763269195, 'joule')>

In [11]: j = _

In [12]: j
Out[12]: <Quantity(17.369415763269195, 'joule')>

In [13]: j / ureg.sq_ft
Out[13]: <Quantity(17.369415763269195, 'joule / square_foot')>

In [15]: j + 2 * ureg.degC                                                   
OffsetUnitCalculusError                   Traceback (most recent call last)  


Lots of units

In [20]: ', '.join(dir(ureg))
Out[20]: 'A, B, BTU, Ba, Bd, Bq, British_horsepower, Btu, C, C12_faraday,
Ci, DPI, Da, EC_therm, E_h, F, Fr, Gy, H, H2O, Hg, Hz, J, K, KPH, L,
Langley, MPH, Measurement, N, N_A, Oe, P, PPCM, PPI, PSH, Pa, P̸, Quantity,
R, Rd, S, St, Sv, T, Tbl, Tblsp, Tbsp, UK_bbl, UK_bushel, UK_cup, UK_cwt,
UK_fluid_ounce, UK_gallon, UK_gill, UK_horsepower, UK_hundredweight,
UK_pint, UK_pk, UK_quart, UK_ton, US_cwt, US_dry_barrel, US_dry_gallon,
US_dry_pint, US_dry_quart, US_fluid_dram, US_fluid_ounce, US_hundredweight,
US_liquid_cup, US_liquid_gallon, US_liquid_gill, US_liquid_ounce,
US_liquid_quart, US_pint, US_shot, US_therm, US_ton, Unit, V, VA, W, Wb, Wh,
Z_0, acre, acre_feet, acre_foot, amp, ampere, ampere_turn, amu, angstrom,
angular_degree, angular_minute, angular_second, ap_dr, ap_lb, ap_oz,
apothecary_dram, apothecary_ounce, apothecary_pound, arc_minute, arc_second,
arcdeg, arcdegree, arcmin, arcminute, arcsec, arcsecond, are,
astronomical_unit, at, atm, atmosphere, atomic_mass_unit, au, avdp_dram,
avdp_ounce, avdp_pound, avogadro_number, avoirdupois_dram,
avoirdupois_ounce, avoirdupois_pound, b, bag, bar, barad, barie, barn,
barrel, barrie, baryd, barye, baud, bbl, becquerel, beer_barrel, beer_bbl,
bit, bits_per_pixel, boiler_horsepower, boltzmann_constant, bpp, bps,
british_thermal_unit, btu, bu, bushel, byte, c, cal, calorie, candela,
candle, carat, cc, cd, celsius, centimeter, centimeter_Hg, ch_cwt, chain,
characteristic_impedance_of_vacuum, chemical_faraday, circle, circular_mils,
cmH2O, cmHg, cm_Hg, cmil, common_year, conventional_mercury,
conventional_water, convert, coulomb, count, counts_per_second, cp, cps,
cu_ft, cu_in, cu_yd, cubic_centimeter, cubic_feet, cubic_foot, cubic_inch,
cubic_yard, cup, curie, cycle, dalton, darcy, day, decitex, define, deg,
degC, degF, degK, degR, degree, delta_degC, delta_degF, denier, dgal, dot,
dots_per_inch, dpi, dqt, dr, drachm, dram, dry_barrel, dry_gallon, dry_pint,
dry_quart, dtex, dwt, dyn, dyne, e, eV, electric_constant,
electric_horsepower, electron_mass, electron_volt, elementary_charge, eon,
 epsilon_0, erg, esu, esu_per_second, fahrenheit, farad, faraday, fathom, feet,
 fine_structure_constant, fldr, floz, fluid_dram, fluid_ounce, fluidram, foot, 
footH2O, foot_H2O, force_gram, force_kilogram, force_ounce, force_pound, 
force_ton, fortnight, franklin, ft, ftH2O, furlong, g, g_0, g_n, gal, gallon,     
gamma, gauss, get_base_units, get_dimensionality, get_name, get_root_units, 
    get_symbol, gf, gi, gilbert, gill, gr, grain, gram, gram_force, gravity, gray, 
gregorian_year, h, h2o, ha, hartree, hartree_energy, hbar, hectare, henry, 
hertz, hogshead, horsepower, hour, hp, hr, hydraulic_horsepower, 
impedance_of_free_space, imperial_barrel, imperial_bbl, imperial_bu, 
imperial_bushel, imperial_cp, imperial_cup, imperial_floz, 
imperial_fluid_drachm, imperial_fluid_dram, imperial_fluid_ounce, imperial_gal,
 imperial_gallon, imperial_gi, imperial_gill, imperial_peck, imperial_pint, 
imperial_pk, imperial_pt, imperial_qt, imperial_quart, in, inHg, in_Hg, inch,
 inch_H2O_39F, inch_H2O_60F, inch_Hg, inch_Hg_32F, inch_Hg_60F, inches, 
international_feet, international_foot, international_inch, 
international_inches, international_knot, international_mile, 
international_steam_table_calorie, international_yard, jig, joule, julian_year, 
k, kelvin, kgf, kilogram, kilogram_force, kilometer, kip, kip_per_square_inch, 
knot, knot_international, kph, ksi, kt, l, langley, lb, lbf, league, leap_year,
 lg_cwt, li, light_year, lightyear, link, liquid_cup, liquid_gallon, 
liquid_gill, liquid_pint, liquid_quart, liter, litre, lm, load_definitions, 
long_hunderweight, long_ton, lumen, lunar_month, lux, lx, ly, m, m_e, m_n, m_p, 
magnetic_constant, maxwell, mercury, mercury_60F, meter, metre,     
metric_horsepower, metric_ton, mho, mi, mil, mile, milenia, milenium, millenia, 
millenium, milligram, milliliter, millimeter, millimeter_Hg, millimeter_Hg_0C, 
min, minim, minute, mmHg, mm_Hg, mol, molar_gas_constant, mole, month, mph, 
mu_0, mx, nautical_mile, nautical_miles_per_hour, neutron_mass, newton, 
newtonian_constant_of_gravitation, nmi, octet, oersted, ohm, oil_barrel, 
oil_bbl, ounce, ounce_force, oz, ozf, parsec, pascal, pc, pdl, peak_sun_hour, peck, 
pel, pennyweight, perch, physical_faraday, pi, pica, picture_element, pint, pixel, 
pixels_per_centimeter, pixels_per_inch, pk, planck_constant, point, poise, pole,
 pond, pound, pound_force, pound_force_per_square_inch, poundal, pp, ppi, 
printers_dpi, printers_pica, printers_point, proton_mass, psi, pt, px, qt, quad, 
quadrillion_btu, quart, quarter, rad, radian, rads, rankine, rd, 
refrigeration_ton, rem, revolution, revolutions_per_minute, rhe, rod, roentgen, 
rpm, rps, rutherford, rydberg_constant, s, scruple, sec, second, sft, shake, 
short_hunderdweight, short_ton, shot, sidereal_day, sidereal_hour, 
sidereal_minute, sidereal_month, sidereal_second, sidereal_year, siemens, 
sievert, slm, slpm, speed_of_light, sq_ft, sq_in, sq_mi, sq_perch, sq_pole, 
sq_rod, sq_yd, square_feet, square_foot, square_inch, square_inches, 
square_mile, square_rod, square_yard, sr, stF, stH, stS, stV, 
standard_atmosphere, standard_gravity, standard_liter_per_minute, statC, statF,
 statH, statS, statV, statampere, statcoulombs, statfarad, stathenry, statmho, 
statohm, statvolt, stefan_boltzmann_constant, steradian, stere, stokes, stone, 
survey_foot, survey_link, survey_mile, synodic_month, t, tTNT, tablespoon, 
tblsp, tbs, tbsp, teaspoon, technical_atmosphere, tesla, tex, th, therm, 
thermochemical_calorie, thm, thou, tlb, toe, ton, ton_TNT, ton_force, 
ton_of_refrigeration, tonne, tonne_of_oil_equivalent, torr, toz, tropical_month,
 troy_ounce, troy_pound, tsp, turn, u, unit_pole, us_statute_mile, 
vacuum_permeability, vacuum_permittivity, volt, volt_ampere, water, water_39F, 
water_4C, water_60F, watt, watt_hour, watthour, weber, week, 
wien_frequency_displacement_law_constant, work_month, work_year, yard, yd, year, 
Å, ångström, ħ, Δcelsius, Δfahrenheit, Ω, π, σ, Å'

Just found one. It's part of sympy. import sympy.physics.units as u.

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