Physical unit converter: 111 quantities and nearly 1,200 units, from SI to traditional

What this converter does

It converts any value between all the units of one quantity and shows the full table at once, so you see the number you were after and, beside it, every other equivalent. It covers 111 quantities and nearly 1,200 units: the International System with its prefixes, imperial and US customary units, the CGS units that survive in electromagnetism, the technical ones (kilopond, metric horsepower, technical atmosphere), the historical ones that still turn up in old documentation, and the traditional Castilian units that remain alive in farming and building in Spain.

The search box at the top finds a unit by name or symbol across every quantity, and the page address stores the conversion (quantity, units and value), so it can be linked or sent to a colleague.

The quantities covered

Electrical and magnetic, the ones most asked for in a test laboratory: current, voltage, resistance, conductance, capacitance, inductance, charge, magnetic flux, flux density, field strength, magnetomotive force, permeability, permittivity, electric field, resistivity, conductivity (including % IACS for copper), current density, magnetic moment and dipole moment. It includes the electromagnetic and electrostatic CGS units (abampere, statvolt, gauss, oersted, maxwell, gilbert), because core catalogues and older manuals still use them.

Levels, signals and transients: power level (dBm, dBW), voltage level (dBV, dBmV, dBµV, dBu) and current level (dBµA), sound pressure (dB SPL), gain and attenuation in decibels, bels and nepers, dV/dt and dI/dt rates of change, surface and volume charge density and magnetic reluctance. Apparent power (VA) and reactive power (var) have quantities of their own, so the converter never turns kvar into kW by mistake.

Mechanical and spatial: length, area (with circular mil and kcmil), volume, mass, time, speed, acceleration, force, pressure and stress, energy, active power (apparent and reactive power have quantities of their own), torque, impulse, mass and area moments of inertia, stiffness, surface tension, density, specific volume, linear and areal density, plane and solid angle, angular velocity and acceleration, frequency and wavenumber.

Materials and testing: jerk, pressure or stress rate (the one in tensile tests, in N/(mm²·s)) and temperature rate (K/min), steel hardness across Vickers, Rockwell C and Brinell, permeability of porous media (darcy), and AWG gauge as both diameter and cross-section.

Thermal: temperature and temperature difference, specific heat, heat capacity, thermal conductivity, heat transfer coefficient, absolute and areal thermal resistance (R-value in European and American units, clo and tog), heat flux density and irradiance, temperature coefficient (ppm/K versus ppm/°F), specific energy, energy density and power density.

Fluids: dynamic and kinematic viscosity, volumetric and mass flow rate and fuel consumption, where the units are reciprocals of one another (L/100 km versus km/L or mpg) and the converter handles it without you having to think about it.

Gases: moisture in gases — ppmv, ppm by weight in air, nitrogen or SF₆, g/m³, lb/MMscf and dew point at 1 atm — and leak rate (Pa·m³/s, mbar·L/s, sccm and grams of SF₆ or helium per year). The empirical viscosity scales (degrees Engler, Saybolt and Redwood seconds) are under “kinematic viscosity”.

Light and radiation: luminous intensity, luminous flux, illuminance, luminance, luminous efficacy, luminous exposure, radiant intensity and radiance; radioactivity, specific activity, activity concentration (radon in Bq/m³ or pCi/L), absorbed dose, equivalent dose, dose rate and exposure.

Others: amount of substance, molar concentration, molality, molar mass, molar flow (with the standard flows sccm, slm, Nm³/h and SCFM), mass concentration, water hardness (°fH, °dH, °e, mmol/L), catalytic activity (katal and enzyme unit), fractions (%, ‰, ppm, ppb, basis points), optical power and focal length, image resolution (dpi, ppi), information in decimal and binary bits and bytes, and data transfer rate.

Where the factors come from

SI units and prefixes follow the SI Brochure (BIPM, 9th edition) and the ISO 80000 series. Non-SI units that are accepted or in common use follow NIST Special Publication 811, the usual reference for conversions to imperial and US customary units. Physical constants (elementary charge, speed of light, electron mass, Bohr magneton, vacuum permeability) are the CODATA 2018 values in force since the 2019 redefinition of the SI.

A few details worth knowing. The calorie has three values in use: thermochemical (4.184 J), International Table or IT (4.1868 J) and the nineteenth-century 15 °C calorie; the converter distinguishes the first two. The BTU has the same problem and is handled the same way. The gallon, pint and fluid ounce exist in US and imperial versions with different values (an imperial gallon is 20% larger). The ton may be metric (1000 kg), short (907 kg) or long (1016 kg). The year may be Julian (365.25 days), common or tropical. And the month used here is the mean month, 30.44 days.

Traditional Castilian units (vara, legua, arroba, fanega, cántara, celemín) had different values by region: the Castile values are given, which were the legal reference from the nineteenth century until the metric system took over.

Scales that are not proportional

Almost every unit converts by multiplying by a factor. A few do not, and the converter handles them with the formula from their standard:

• Decibels. A level in dB compares against a reference: 10·log₁₀ for power (dBm, relative to 1 mW; dBW, to 1 W) and 20·log₁₀ for amplitudes (dBV, dBµV, dBu, dB SPL, relative to 20 µPa). The neper uses the natural logarithm of the amplitude ratio: 1 Np = 8.686 dB. Under “gain and attenuation” you can enter either the power ratio or the amplitude ratio, and the converter applies the square root that separates them.
• Dew point. Calculated with the Buck equations at atmospheric pressure (1013.25 hPa), over ice below 0 °C, which is what chilled-mirror hygrometers measure; a second unit assumes supercooled water. For another measuring pressure, the SF₆ calculator makes the correction.
• AWG. The diameter is d = 0.127 mm · 92^((36 − n)/39) (ASTM B258). Heavy gauges are written as in the catalogue: 1/0, 2/0, 3/0 or 4/0.
• Hardness. Vickers, Rockwell C and Brinell (10 mm carbide ball, 3000 kgf) are related through Table 1 of ASTM E140 for non-austenitic steels, between 20 and 65 HRC. It is an approximate equivalence and gives no value outside that range.
• Empirical viscosity. Degrees Engler by the Ubbelohde formula (ν = 7.31·E − 6.31/E cSt), Saybolt universal seconds by ASTM D2161 at 100 °F and Redwood No. 1 seconds by the two usual empirical formulas.
• Gas flows and masses. Standard units (sccm, slm, Nm³/h, SCFM) and grams per year of SF₆ or helium assume an ideal gas at the conditions stated in each name.

When a value falls outside the range of one of these scales, the cell shows “—” instead of extrapolating.

Worked example

A North American motor nameplate reads 25 hp and it has to be compared with a European 18.5 kW motor. Under “power”, 25 hp (mechanical) = 18.64 kW: they are equivalent. Had the plate said 25 PS or CV, it would be 18.39 kW, slightly below.

A magnetic core catalogue gives saturation as 12 000 G and coercive force as 0.8 Oe. In SI: 12 000 G = 1.2 T; 0.8 Oe = 63.7 A/m.

An American gauge reads 145 psi. Under “pressure and stress”: 145 psi = 10.0 bar = 1.00 MPa = 9.87 atm = 10.2 kgf/cm².

An IEEE table gives a thermal expansion coefficient of 9.4 ppm/°F. Under “temperature coefficient”: 9.4 ppm/°F = 16.9 ppm/K, which is the coefficient of copper.

A partial discharge detector gives its signal as 60 dBµV. Under “voltage level”: 60 dBµV = 1 mV = −60 dBV.

A hygrometer reads a dew point of −36 °C in SF₆ at atmospheric pressure. Under “moisture in gases”: 198 ppmv, which by weight is 24 ppmw in SF₆.

A helium tightness test gives a leak of 1 × 10⁻⁶ mbar·L/s. Under “gas leak rate”, that is 0.19 g of SF₆ per year, the figure that emission limits for fluorinated gases are compared against.

What this converter does not do

It does not convert between different quantities: it will not go from kilowatts to amperes or from frequency to wavelength, because that needs one more datum (the voltage, the propagation velocity) and is no longer a unit conversion. For the same reason it will not go from dBm to dBµV: that needs the impedance (at 50 Ω, dBµV = dBm + 107). Dew point is given at atmospheric pressure; for another pressure, use the SF₆ calculator. Left out are scales with no physical equivalence to another unit — pH, astronomical magnitudes, Beaufort, the Mohs scale, which only ranks minerals — and Rockwell B hardness, whose published tables disagree too much to give a reliable number. Currencies are not physical units and are not included. Nor are local units from outside Castile or the historical variants of each unit: where an old unit had several values, only the one adopted as the reference appears.

What it relates to

The equivalence between kcmil, AWG and mm² is the one applied by the cable size calculator in this same section. The tesla, gauss and oersted conversions are the ones needed to read the datasheets of current transformers and cores tested with transformer test equipment, and the resistivity and conductivity conversions help interpret the reading of a micro-ohmmeter or an earth tester. For full geographic positions — latitude and longitude, UTM and ED50 to ETRS89 — there is the coordinate converter; under “plane angle” this converter also reads and writes degrees, minutes and seconds.