MathBench

Engineering Unit Converter

Pick a quantity, type a value in either field, and read the answer, plus the same value in every unit, the exact factor used, and where that factor comes from.

7

Same value in every unit

UnitNameValue

Factors used:

UnitValue in base unitHow it is defined

Exact means the factor is exact by definition and its decimal expansion terminates. Where a defined ratio has a repeating decimal (e.g. psi), the value is still exact by definition but shown truncated. Arithmetic runs in IEEE 754 double precision, good to about 15–16 significant digits.

Where these numbers come from

    How this calculator works

    The quickest way in is the search box: type a unit the way you would say it and the converter jumps there. One unit (kips, kg·m/s, psi) loads that quantity and puts the unit in the "From" box; a pair like m to ft sets both sides at once, and you can lead with a number, as in 5 kg to lb. Plurals, US spellings and the usual shorthands are understood, and if two units belong to different quantities the box says so.

    Choose the quantity you're converting from one grouped dropdown (geometry, mechanics, fluids, thermal, motion), then type a value in either field. The other updates instantly, and the table below shows the same value expressed in every unit of that quantity at once. The digits slider controls display precision, and the swap button flips the direction.

    What makes this converter different is that it shows its work. The "factors used" table lists the exact factor behind every unit and how it is derived from a defining constant (the 1959 inch, standard gravity, the standard atmosphere), and the sources block cites the documents those constants come from. Nothing here was copied from another conversion website.

    The formula

    value in base unit = value × factor  (+ offset, temperature only)
converted value    = (base − offset₂) ÷ factor₂

    Every unit is defined by one exact factor to its quantity's SI base unit, and every conversion is two steps through that base. Temperature is the one affine case: Fahrenheit and Celsius have shifted zeros, so the conversion includes an offset. Factors were derived by exact arithmetic from defining constants and cross-checked against NIST SP 811 Appendix B.9.

    Worked example

    Say a datasheet gives a burst pressure of 30 psi and you need kPa:

    1. 1 psi = 4.4482216152605 N ÷ 0.00064516 m² = 6,894.757… Pa (exact by definition, non-terminating decimal)
    2. 30 psi = 30 × 6,894.757 = 206,842.7 Pa
    3. In kilopascals: 206.84 kPa

    Every step is visible in the tool: the equation line shows the factor, and the factors table shows where 4.4482216152605 and 0.00064516 come from (the 1959 pound and inch, and standard gravity).

    Assumptions & tips

    • The "exact" tags mean what they say. Most customary units have been defined as exact multiples of SI since 1959. An inch is 25.4 mm by definition, not by measurement. "Truncated" means the exact ratio has a repeating decimal, not that the factor is uncertain.
    • Temperature converts with an offset. Doubling 20 °C does not give twice the temperature. For ratios, work in kelvin. The equation line shows both the slope and the zero point when temperature is selected.
    • Watch the two Btus and two calories. The International Table and thermochemical definitions differ by ~0.07%. HVAC uses IT. Combustion chemistry often uses thermochemical. Both are listed.
    • MPa and N/mm² are the same number. As are cSt and mm²/s, and cP and mPa·s, the table view makes these identities visible instead of asking you to memorize them.
    • Second moment of area is not mass moment of inertia. Both get called "moment of inertia". One is length⁴ (beam bending), the other mass × length² (rotation). They're separate quantities here, each with a note pointing to the other.

    Frequently asked questions

    Why do most factors say "exact"?

    Because they are defined, not measured. Since the 1959 International Yard and Pound Agreement, an inch is exactly 25.4 mm and a pound exactly 0.45359237 kg. The standard atmosphere, the calorie, and the electronvolt are likewise fixed by definition. Every factor here is derived from those defining constants by exact arithmetic and cross-checked against NIST Special Publication 811. The tables under the converter show the derivation for each unit.

    What is the difference between torr and mmHg?

    Two definitions that nearly coincide. The torr is exactly 1/760 of a standard atmosphere. The conventional millimetre of mercury is a 1 mm column of idealized mercury under standard gravity. They differ by about 0.15 parts per million (far below the accuracy of any gauge you will read), but both are listed so you can match whichever your datasheet cites.

    Why does temperature behave differently from other quantities?

    Temperature scales have different zero points, not just different step sizes, so converting is an offset plus a scale: 0 °C is 32 °F, not 0 °F. The converter handles this automatically, and the equation line shows both the slope and the offset when temperature is selected. Every other quantity on the page converts through a pure ratio.

    How many digits of the result can I trust?

    The factors themselves are exact or correctly rounded, and the arithmetic runs in IEEE 754 double precision: good to about 15 to 16 significant digits. The digits slider controls display rounding only. In practice your measurement is the limiting factor: a tape measure is 3 digits on a good day, so showing 7 is already generous.

    What happened to the US survey foot?

    It was deprecated at the end of 2022. All foot-derived units here use the international foot (exactly 0.3048 m), and the acre is the international acre, about 16 parts per million smaller than the old survey acre. The difference is only significant in land surveying at state-plane coordinate scales. For engineering work the international values are the current standard.

    Sources

    1. NIST Special Publication 811, Guide for the Use of the International System of Units (SI), 2008 edition. National Institute of Standards and Technology. nvlpubs.nist.govAppendix B.9 is the table every factor on this page was cross-checked against, including the International Table calorie and Btu, the therm, and the customary units derived from them.
    2. The International System of Units (SI), 9th edition. Bureau International des Poids et Mesures, 2019. bipm.orgThe SI prefixes and base-unit definitions, and the exact elementary charge 1.602176634 × 10⁻¹⁹ C that fixes the electronvolt.
    3. Refinement of Values for the Yard and the Pound. National Bureau of Standards notice, Federal Register 24 FR 5348, 30 June 1959. ngs.noaa.govThe International Yard and Pound Agreement as announced for the United States: 1 yd = 0.9144 m and 1 lb = 0.45359237 kg exactly, from which the inch, foot and every derived customary factor here follows.
    4. Resolution 2 of the 3rd CGPM (1901). Conférence Générale des Poids et Mesures. bipm.orgFixes standard gravity at gₙ = 9.80665 m/s² exactly: the constant that turns kilograms and pounds into kilogram-force and pound-force, and that defines the conventional mercury and water pressure columns.
    5. Resolution 4 of the 10th CGPM (1954). Conférence Générale des Poids et Mesures. bipm.orgDefines the standard atmosphere as exactly 101 325 pascals, from which the torr follows as 1/760 atm.
    6. NIST Handbook 44, Appendix C — General Tables of Units of Measurement. National Institute of Standards and Technology, 2026 edition. nist.govThe US liquid gallon as exactly 231 cubic inches, which fixes the gallon, quart, fluid ounce and every US flow unit on this page.
    7. Weights and Measures Act 1985, Schedule 1. United Kingdom Parliament. legislation.gov.ukDefines the imperial gallon as exactly 4.54609 litres, distinguishing it from the US gallon in the volume and flow tables.
    8. Deprecation of the United States (U.S.) Survey Foot. NIST and NOAA National Geodetic Survey, Federal Register 85 FR 62698, 5 October 2020. govinfo.govWhy every foot-derived unit here uses the international foot of exactly 0.3048 m, and why the survey acre appears only as a note.
    9. ISO 80000-4, Quantities and units — Part 4: Mechanics; and ISO 80000-5, Part 5: Thermodynamics. International Organization for Standardization. The conventional pressure columns: 1 mmHg from a fixed density of 13 595.1 kg/m³ and 1 mH₂O from 1000 kg/m³, both under standard gravity.