What is physics unit conversion?
A unit is a magnitude against which a physical quantity is measured, and unit conversion is the arithmetic of comparing one such magnitude with another. The international standard since 1960 has been the Système International d'Unités (SI), organized around seven base units — the meter, kilogram, second, ampere, kelvin, mole, and candela — from which every other unit is derived by multiplication or division. A coherent unit system means the product or quotient of quantities gives the product or quotient of their units, so the equation J = N·m works without inserting magic constants. A non-coherent system like CGS inserts such constants — useful historically, awkward in practice. The panel keeps everything in SI factors: each unit is stored as one number (the factor to convert to the SI base), and every answer is unit_in_SI ÷ unit_out_in_SI, with formatting handled by the display layer.
SI gives you one base unit per quantity, the panel gives you every other as a factor: 1 km = 10³ m, 1 parsec = 3.0857×1016 m, 1 electronvolt = 1.602×10−19 J. The conversion factor is the entire physics of the conversion; everything else is the format.
Length — from Ångström to parsec
The panel's 16 length entries span about 26 orders of magnitude, from the Ångström (10−10 m, the scale of chemical bonds and atomic spacings) to the parsec (3.0857×1016 m). The metre is the working SI unit; everything else is just a naming convention with a fixed factor. Inside the same magnitude range, working units differ by discipline: nanometres for wavelengths of visible light (400-700 nm); micrometres for cell biology; millimetres for mechanical engineering; centimetres for everyday objects; kilometres for geography. For the human-to-Earth-to-galaxy scale, the astronomical unit (1 AU = 1.496×1011 m, exactly defined as the Earth-Sun distance) and light-year (1 ly = 9.461×1015 m, the distance light travels in a Julian year) bridge the solar system to the nearest stars. Parsecs are the professional astronomy unit, defined as the distance at which 1 AU subtends one arc-second: 1 pc ≈ 3.26 ly ≈ 206,265 AU.
Mass — from yoctogram to solar mass
Twelve mass entries cover the physics-from-quantum to astronomy range: the atomic mass unit (1.661×10−27 kg, one Dalton, the mass of a nucleon) for chemistry, micrograms and milligrams for analytical chemistry, the kilogram for everyday use, tonnes for industrial quantities, the avoirdupois pound (0.4536 kg, exactly defined since 1959 as 453.59237 g), and the solar mass (1.989×1030 kg) for stars. The carat (200 mg exactly) is the mass unit for gemstones; the slug (14.594 kg) is the imperial mass unit that gives F = ma in pounds-force without extra factors — useful if you must work in US customary. Note that "weight" is technically a force, not a mass; a kilogram-force is 9.81 N. The panel does not confuse the two: every entry here is a mass in kg.
Energy — joule, eV, calorie, BTU, kWh
The energy column spans the gap between quantum (electron-volt, 1.602×10−19 J) and industrial (kilowatt-hour, 3.6×106 J). The SI unit is the joule (1 J = 1 N·m = 1 kg·m²/s²); the electron-volt is the natural atomic unit (the kinetic energy an electron gains traversing 1 volt); the calorie (4.184 J, thermochemical) lives on in nutrition labels; the British thermal unit (1 BTU ≈ 1,055 J) survives in HVAC ratings and the energy of a single wooden kitchen match; and the kWh is what shows up on your electricity bill. E = mc² ties mass and energy directly: 1 kg of mass holds 8.988×1016 J, enough to run the entire world economy for a few seconds. The food Calorie (note the capital) is actually a kilocalorie (1,000 cal = 4,184 J).
Pressure — pascal, atm, bar, mmHg, psi
Pressure has more units than almost any other physical quantity because it grew up in three traditions at once: meteorology (millimetres of mercury, mmHg, and millibars), engineering (pounds per square inch, psi), and physics (pascal, Pa = N/m²). Anchoring numbers: 1 atm = 101,325 Pa exactly — the original SI unit was the "standard atmosphere"; 1 mmHg ≈ 133.322 Pa (the height of a 1 mm column of mercury at standard gravity); 1 bar = 100,000 Pa exactly (a practical round number, slightly less than 1 atm); 1 psi ≈ 6,894.76 Pa. The mmHg-to-Pa ratio is what makes a mercury barometer work: 760 mmHg = 1 atm. Blood pressure is conventionally reported in mmHg, atmospheric in hPa (hectopascals, equal numerically to millibars), and tire pressure in psi.
Temperature is special
Every other quantity's conversion is a single multiplicative factor. Temperature is the exception: its units differ by an offset as well as a scale, because 0 in each scale is a different place. To convert from Celsius to Kelvin, add 273.15; from Fahrenheit to Rankine, add 459.67; from Celsius to Fahrenheit, multiply by 9/5 and add 32. To convert a temperature difference use only the scale factor (1 K = 1°C = 9/5°F). The panel handles this with category-specific scaling and offset so that 100°C reads as 212°F (not 180°F, the common mistake). Mistaking temperature differences for temperatures is the single most common error in unit conversion.
Miscellaneous: angles, charge, voltage, frequency
A few conversions are worth flagging because they catch out even experienced people: radians and degrees are not just dimensionless, they are the same dimensionless — 2π radians = 360°, with one full circle of either unit being a ratio of length/radius that comes out as a pure number; this is why ω in angular formulas can take either unit. Frequency is the inverse of time: hertz = 1/s. Voltage (a joule per coulomb) and electric charge (coulombs) are linked to current (amperes) by Q = I·t. The base unit for current, the ampere, is defined as 6.241×1018 elementary charges per second; the recent 2019 SI redefinition swapped that to a fixed value for the elementary charge and derived the ampere. The panel uses conventional engineering factors throughout, which match the practical definitions to better than a part per million for almost all purposes.
Common misconceptions
- Temperature is just a different scale, like inches vs centimetres. Temperature scales are offset as well as scaled: 0°C = 273.15 K, not 0 K. A 1 K interval equals a 1°C interval, but the absolute temperatures are different. Mixing these is the most common error in unit conversion involving heat.
- A pound is a kilogram. A pound is a unit of mass in the avoirdupois system (exactly 0.453 592 37 kg since 1959); a pound-force (lbf) is a unit of force (about 4.45 N). They differ by a factor of g ≈ 9.81. Bodyweight scales report pounds-mass; rocket engines report pounds-force; both are correct in their own context.
- 1 kg of weight is converted by 9.81 to get Newtons. 9.81 m/s² is the standard surface gravity, not the conversion factor. 1 kg of mass weighs about 9.81 N at sea level, but the same mass is the same number everywhere — the weight (force) is what depends on local g.
- The electron-volt is a unit of voltage. Despite the name, eV is a unit of energy: the energy an electron gains moving through a potential of one volt. 1 eV = 1.602×10−19 J. This makes the "volt" inside "eV" a kinematic convenience, not a force unit.
Related tools: Constants Reference for the values underlying these factors, Thermodynamics for the special temperature case in action, and Calculator for the algebra of dimensional analysis.
