Unit System Overview
ExprUA uses a comprehensive unit system based on the International System of Units (SI). All units are internally converted to base SI units, ensuring dimensional consistency and automatic unit conversion.
How Units Are Derived
Units in ExprUA follow a hierarchical derivation system:
- Base SI Units: Seven fundamental units (kg, m, s, A, K, mol, cd) form the foundation
- Derived Units: Created by combining base units using multiplication and division (e.g., N = kg⋅m/s²)
- Unit Variants: Multiple names and aliases map to the same underlying unit (e.g., "meter", "metre", "m")
- Unit Prefixes: SI prefixes (kilo, milli, etc.) can be applied to compatible units
When you use a unit in ExprUA, the system:
- Identifies the unit from its name or alias
- Converts it to the equivalent base SI representation
- Performs calculations with dimensional consistency checking
- Displays results in the most appropriate unit format
Base SI Units
The International System of Units (SI) defines seven base units from which all other units are derived:
kg - kilogram (mass)m - meter (length)s - second (time)A - ampere (electric current)K - kelvin (temperature)mol - mole (amount of substance)cd - candela (luminous intensity)
SI Prefixes
SI prefixes can be applied to compatible units to create scaled versions. For example, kilometer (km), milligram (mg), microsecond (µs). The following prefixes are supported:
- quetta (Q) - 10³⁰
- ronna (R) - 10²⁷
- yotta (Y) - 10²⁴
- zetta (Z) - 10²¹
- exa (E) - 10¹⁸
- peta (P) - 10¹⁵
- tera (T) - 10¹²
- giga (G) - 10⁹
- mega (M) - 10⁶
- kilo (k) - 10³
- hecto (h) - 10²
- deca (da, deka) - 10¹
- deci (d) - 10⁻¹
- centi (c) - 10⁻²
- milli (m) - 10⁻³
- micro (u, µ) - 10⁻⁶
- nano (n) - 10⁻⁹
- pico (p) - 10⁻¹²
- femto (f) - 10⁻¹⁵
- atto (a) - 10⁻¹⁸
- zepto (z) - 10⁻²¹
- yocto (y) - 10⁻²⁴
- ronto (r) - 10⁻²⁷
- quecto (q) - 10⁻³⁰
Note: Prefixes are automatically generated for compatible units. For example, all length units (m, cm, km, mm, etc.) and all time units (s, ms, µs, ns, etc.) are available with these prefixes.
SI Units
Base and derived units from the International System of Units
- ampere (A)
- becquerel (Bq)
- candela (cd)
- coulomb (C)
- farad (F)
- gray (Gy)
- henry (H)
- hertz (Hz)
- joule (J)
- katal (kat)
- kelvin (K)
- kilogram (kg)
- liter (litre, L)
- lumen (lm)
- lux (lx)
- meter (metre, m)
- mole (mol)
- newton (N)
- ohm
- pascal (Pa)
- second (s)
- siemens (S)
- sievert (Sv)
- tesla (T)
- volt (V)
- watt (W)
- weber (Wb)
Metric Units
Metric system units including length, mass, and volume
- angstrom (ang)
- are (ares)
- astronomical_unit (au, AU)
- barn (barns)
- cubic_centimeter (cc, cm3, ccm, cubic_cm)
- fermi (fm, femtometer, fermis)
- hectare (ha, hectares)
- lambda
- light_year (ly, lightyear, light_years)
- liter (litre, l, L, liters, litres)
- metric_ton (tonne, t, metric_tons, tonnes)
- micron (micrometer, um, microns)
- parsec (pc, parsecs)
- stere (st, steres, cubic_meter, cubic_metre)
- unified_atomic_mass_unit (amu, atomic_mass_unit)
US Customary Units
United States customary units (USCS)
- BTU (british_thermal_unit)
- bushel (bu, US_bushel, US_bu)
- chain (chains)
- cup (cp, US_cup)
- dry_gallon (dgal, US_dry_gallon)
- dry_quart (dqt, US_dry_quart)
- fathom (fathoms)
- fluid_ounce (floz, US_fluid_ounce, US_floz)
- foot (ft, feet, international_foot)
- gallon (gal, US_liquid_gallon, US_gal)
- gill (gi, US_gill, US_gi)
- hand (hands)
- hundredweight (cwt, short_hundredweight, US_cwt)
- inch (in, inches, international_inch, ")
- link (links)
- mile (mi, miles, international_mile)
- ounce (oz, ounces, avoirdupois_ounce, US_oz)
- peck (pk, US_peck, US_pk)
- pint (pt, US_liquid_pint, US_pt)
- pound (lb, pounds, avoirdupois_pound, US_lb)
- pound_force (lbf, US_lbf)
- poundal (pdl, US_pdl)
- quart (qt, US_liquid_quart, US_qt)
- rod (rods, pole, perch)
- stone (st, stones, US_st)
- tablespoon (tbsp)
- teaspoon (tsp)
- thou (th, mil_length)
- ton (short_ton, US_ton)
- yard (yd, yards, international_yard)
Imperial Units
British Imperial units
- bushel (imperial_bushel, impbu, imp_bu, UK_bushel, UK_bu)
- chain (chains)
- fathom (fathoms)
- fluid_ounce (imperial_fluid_ounce, impfloz, imp_floz, UK_fluid_ounce, UK_floz)
- foot (ft, feet, imperial_foot)
- gallon (imperial_gallon, impgal, imp_gal, UK_gallon, UK_gal)
- gill (imperial_gill, impgi, imp_gi, UK_gill, UK_gi)
- hand (hands)
- hundredweight (imperial_hundredweight, impcwt, imp_cwt, UK_hundredweight, UK_cwt)
- imperial_ton (impton, imp_ton, UK_ton)
- inch (in, inches, imperial_inch, ")
- link (links)
- mile (mi, miles, imperial_mile)
- ounce (ounces, imperial_ounce, impoz, imp_oz, UK_ounce, UK_oz)
- peck (imperial_peck, imppk, imp_pk, UK_peck, UK_pk)
- pint (imperial_pint, imppt, imp_pt, UK_pint, UK_pt)
- pound (pounds, imperial_pound, implb, imp_lb, UK_pound, UK_lb)
- pound_force (implbf, imp_lbf, UK_lbf)
- poundal (imppdl, imp_pdl, UK_pdl)
- quart (imperial_quart, impqt, imp_qt, UK_quart, UK_qt)
- rod (rods, pole, perch)
- stone (stones, impst, imp_st, UK_stone, UK_st)
- thou (th, mil_length)
- ton_force (imperial_ton_force)
- yard (yd, yards, imperial_yard)
Atomic Units
Natural units used in atomic physics
- atomic_current (au_current)
- atomic_electric_dipole_moment (au_electric_dipole_moment)
- atomic_electric_field (au_electric_field)
- atomic_electric_potential (au_electric_potential)
- atomic_electric_quadrupole_moment (au_electric_quadrupole_moment)
- atomic_force (au_force)
- atomic_intensity (au_intensity)
- atomic_magnetic_dipole_moment (au_magnetic_dipole_moment)
- atomic_magnetic_flux_density (au_magnetic_flux_density)
- atomic_magnetizability (au_magnetizability)
- atomic_permittivity (au_permittivity)
- atomic_temperature (au_temperature)
- atomic_time (au_time)
- atomic_velocity (au_velocity)
- bohr (a0)
- bohr_radius (a0, bohr, atomic_length, au_length)
- electron_mass (me, atomic_mass, au_mass)
- elementary_charge (e, atomic_charge, au_charge)
- hartree (Eh, atomic_energy, au_energy)
- hartree_energy (E_h)
- reduced_planck_constant (hbar, au_angular_momentum)
- rydberg (Ry, rydberg_energy)
Dimensionless Units
Units for dimensionless quantities like percentages
- dimensionless
- percent
- permille (per_mille)
- ppb (parts_per_billion)
- ppm (parts_per_million)
Electrical Units
Electrical energy and charge units
- ampere_hour (Ah)
- watt_hour (Wh)
Planck Units
Natural units based on fundamental physical constants
- planck_acceleration (a_P, a_planck, pl_acceleration)
- planck_area (A_P, A_planck, pl_area)
- planck_charge (q_P, q_planck, pl_charge)
- planck_current (I_P, I_planck, pl_current)
- planck_density (rho_P, rho_planck, pl_density)
- planck_energy (E_P, E_planck, pl_energy)
- planck_force (F_P, F_planck, pl_force)
- planck_impedance (Z_P, Z_planck, pl_impedance)
- planck_length (l_P, l_planck, pl_length)
- planck_mass (m_P, m_planck, pl_mass)
- planck_momentum (p_P, p_planck, pl_momentum)
- planck_power (P_P, P_planck, pl_power)
- planck_pressure (p_P, pl_pressure)
- planck_temperature (T_P, T_planck, pl_temperature)
- planck_time (t_P, t_planck, pl_time)
- planck_voltage (V_P, V_planck, pl_voltage)
- planck_volume (Vol_P, Vol_planck, pl_volume)
Temperature Units
Temperature scales (Celsius, Reaumur)
- celsius (degC, degree_Celsius, degreeC)
- reaumur (degRe, degree_Reaumur, degreeRe)
Time Units
Various time units from seconds to eons
- century (cent, cents, centuries)
- common_year (comm_yr, common_years)
- day (d, days)
- decade (dec, decs, decades)
- eon (eons)
- fortnight (fn, fortnights)
- gregorian_year (greg_yr, gregorian_years)
- hour (h, hr, hrs)
- leap_year (leap_yr, leap_years)
- millennium (mill, mills, millennia)
- minute (min, mins)
- month (mo, mos, months)
- shake (shakes)
- sidereal_day (sid_day, sidereal_days)
- sidereal_month (sid_mo, sidereal_months)
- sidereal_year (sid_yr, sidereal_years)
- svedberg (sved, svedbergs)
- synodic_month (syn_mo, synodic_months, lunar_month, lunar_months, lunation)
- tropical_month (trop_mo, tropical_months)
- tropical_year (trop_yr, tropical_years)
- week (wk, wks, weeks)
- year (a, yr, yrs, julian_year, julian_years)