Unit Converter

Most of these numbers are definitions, not measurements

NIST sets conversion factors in boldface when the printed digits are exact, and four of the length factors behind the panel above are in boldface: inch to metre 2.54 E-02, foot to metre 3.048 E-01, yard to metre 9.144 E-01, mile to metre 1.609 344 E+03.

So 1 in = 2.54 cm is not a careful measurement that a better laboratory might improve. It is an agreement about what the word inch means, and converting inches to centimetres introduces no error at all. The same is not true of every row in the list above, and the rows where it is not true are the ones worth reading about.

The foot changed on 1 January 2023, and hardly any converter says so

Until the end of 2022 the United States had two feet in legal use, differing by a hair, and a long record of nobody being sure which one a given document meant. A Federal Register notice (85 FR 62698, 5 October 2020) ended it: “Beginning on January 1, 2023, the U.S. survey foot should not be used and will be superseded by the ‘international foot’ definition”. NIST’s own summary is flatter still: “January 1, 2023 – The U.S. survey foot is deemed obsolete and superseded by the international foot.”

The two values, both from NIST: the retired US survey foot was “1 foot = 1200/3937 meter exactly (or 1 foot = 0.304 800 6 meter approximately)”, and the international foot is “1 foot = 0.304 8 meter exactly”. Divide one by the other and the survey foot is longer by exactly 2 parts per million. The notice quantifies what that costs you: “the 2 parts per million difference in length (approximately 0.01 foot per mile)”, and for area, “the difference in area for 1 acre is only 0.000 004 acre (about 0.17 ft² or 25 square inches)”.

Two parts per million is nothing for a kitchen shelf and quite a lot for a State Plane coordinate, where values run to millions of feet and the discrepancy becomes metres. Over a 100,000-foot traverse it is 0.2 ft. The notice attributes the whole change to “a long history of misunderstandings and confusion over which definition of the foot was used to carry out a specific land survey or civil engineering project”.

The ft in the panel above is the international foot, 0.3048 m exactly, which is the current and correct one. If you are converting a figure off a plat, a deed or a survey drawn before 2023, find out which foot it was written in first. No converter can tell from the number.

Mass and weight are different quantities, and this page converts mass

NIST SP 811 is precise about a word most of us use loosely. In its scientific sense, “the weight of a body in a particular reference frame is defined as the force that gives the body an acceleration equal to the local acceleration of free fall”, and “the SI unit of the quantity weight defined in this way is the newton (N)”. Then it concedes the ordinary sense: “In commercial and everyday use, and especially in common parlance, weight is usually used as a synonym for mass. Thus the SI unit of the quantity weight used in this sense is the kilogram (kg)”. Its instruction is to prefer the unambiguous word, that “the word ‘mass’ should be used instead”, and that “whenever the word ‘weight’ is used, it should be made clear which meaning is intended”.

Taking that instruction seriously: the category labelled Weight above converts mass. Kilogram, gram, milligram, pound, ounce and tonne are all units of mass. The newton is not in the list, and could not usefully be, because turning a mass into a force needs a local value for the acceleration of free fall, which varies with where you are standing. A two-pan balance compares masses and gives the same answer anywhere; a spring bathroom scale senses force and reports a mass by assuming it is on Earth.

Every volume unit here is the US one, and that matters by a fifth

NIST lists the two gallons as separate units with separate factors: gallon (U.S.) is 3.785 412 E-03 m³, and gallon [Canadian and U.K.] is 4.546 09 E-03 m³, printed in boldface, so exact. The imperial gallon is 20.09% larger. Ten imperial gallons are 45.46 L; ask this page and you are told 37.85 L, short by 7.6 L. Nothing in the input 10 gal distinguishes the two cases.

Now the part that catches people who know about the gallons. NIST gives fluid ounce (U.S.) as 2.957 353 E-05 m³ and the Canadian and U.K. fluid ounce as 2.841 306 E-05 m³. The imperial fluid ounce is smaller than the US one, by 3.92%, even though the imperial gallon is 20% bigger. Both facts hold because the two gallons are cut into different numbers of pieces, and NIST’s own figures divide out to exactly the integers you would hope for:

• 3785.411784 mL ÷ 29.5735295625 mL = 128 US fluid ounces per US gallon;
• 4546.09 mL ÷ 28.4130625 mL = 160 imperial fluid ounces per imperial gallon.

The practical reading of that: a recipe quantity in fluid ounces survives the wrong choice of system with about a 4% error, which you may never notice. A fuel or tank figure in gallons does not: 20% of a 15 gallon tank is three gallons. gal, qt, pt, cup and floz in the list above are all US customary, and each of their values matches NIST’s US factor to every digit NIST prints.

t is the tonne, not the ton

The BIPM’s SI Brochure lists the tonne among the non-SI units accepted for use with the SI, as “1 t = 1 Mg = 10³ kg”, with a footnote recording that “The tonne and its symbol, t, were adopted by the CIPM in 1879” and that it “is sometimes referred to as ‘metric ton’ in some English-speaking countries”.

The US short ton is a different unit. NIST gives “ton, short (2000 lb)” as 9.071 847 E+02 kg against “ton, metric (t)” at 1.0 E+03 kg, boldface and therefore exact. The tonne is 10.23% heavier. The t above is the tonne, so if you pick it while thinking of a ton of gravel, the converted figure comes out roughly 10% high. Twenty short tons is 40,000 lb; twenty tonnes is 44,092 lb.

Temperature is the one category where the arithmetic is different

Length, mass and volume all convert by multiplying by a constant: double the input and the output doubles. Temperature scales carry an offset instead of starting from a shared zero, and three things follow that catch people out.

The kelvin scale starts at the bottom. The SI Brochure defines it by physics rather than by a reference substance: the kelvin “is defined by taking the fixed numerical value of the Boltzmann constant, k, to be 1.380 649 × 10⁻²³ when expressed in the unit J K⁻¹”. Zero kelvin is the floor of thermodynamic temperature, so there is no temperature below it to report: 0 K is −273.15 °C and −459.67 °F, and nothing is colder.

An interval is not a temperature. The Brochure gives the conversion as “t/°C = T/K − 273.15” for a temperature, but adds that “A difference or interval of temperature may be expressed in kelvins or in degrees Celsius, the numerical value of the temperature difference being the same in either case.” So a rise of 5 °C is a rise of 5 K, while a temperature of 5 °C is 278.15 K. The panel above converts temperatures. Put an interval through it and the answer is wrong by 273.15.

You cannot scale a temperature. “Twice as warm” has no meaning on the Celsius or Fahrenheit scales, because their zeros are arbitrary. 20 °C and 10 °C are 293.15 K and 283.15 K, a ratio of 1.035, not 2. Ratios of temperatures are only defined on the kelvin scale, and almost nobody who says “twice as hot” means 586.3 K.

One pleasing consequence of the offsets: −40 is the single point where the Celsius and Fahrenheit scales cross, so −40 °C is −40 °F exactly. Check it against the formula the panel uses, −40 × 9/5 + 32 = −72 + 32 = −40.

What this converter does not know

How many digits your number deserved. The result carries ten significant figures, which is not the same thing as rounding to your significant figures. 1 in = 2.54 cm is exact, but an inch read off a tape measure is not exactly an inch, and the converter cannot tell a defined quantity from a measured one. Ten digits of a figure you read to the nearest eighth of an inch does not make it more accurate, only longer.

Until 7 October 2026 it rounded to eight DECIMAL PLACES instead, which is a different thing and wrong at both ends of the scale. Anything below 5×10⁻⁹ disappeared: 1 mg to t printed “0 t” when the answer is 10⁻⁹ t, and 1 mg to lb showed two significant figures where the answer has far more. At the other end a floating-point artifact survived the rounding, so 10²¹ m to mm read 1.0000000000000001×10²⁴. No fixed decimal count can be right across twenty orders of magnitude, which is why the format is now counted in significant figures.

Which system you meant. As above, for gal and for t. A unit symbol is not always a unique unit, and a converter that accepts a symbol has already guessed.

Force, pressure or anything derived. There is no newton here and no conversion from mass to force, for the reason given above. Nor is there any unit of area or energy, so square feet and kilowatt-hours are out of scope rather than merely missing.

Which cup you had in mind. The cup row is the US customary cup, 0.2365882365 L, which is NIST’s “cup (U.S.)” at 2.365 882 E-04 m³. Other definitions of a cup circulate in cookery and on packaging, and this page carries only that one.

What a historical document meant. Units get redefined, as the foot was in 2023, and a converter only ever applies today’s definitions. For anything legal, surveyed or old, the date on the document is part of the data.

Sources

• NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B.8 — every conversion factor quoted above, the boldface convention marking a factor exact, and the separate entries for the US and the Canadian/UK gallon and fluid ounce, and for the short ton against the metric ton. Each factor in the panel was checked against this table.
• NIST Special Publication 811, section 8.3, mass and weight — weight as a force in newtons, the everyday use of the word to mean mass in kilograms, and the instruction to say which is meant.
• Deprecation of the United States (U.S.) Survey Foot, 85 FR 62698, 5 October 2020 — the 1 January 2023 date, the supersession by the international foot, the 2 parts per million figure, the 0.01 foot per mile and 0.17 ft² per acre consequences, and the reason given for the change.
• NIST, U.S. Survey Foot: Revised Unit Conversion Factors — both exact definitions, 1200/3937 m for the survey foot and 0.3048 m for the international foot.
• BIPM, The International System of Units (SI Brochure), 9th edition — the definition of the kelvin via the Boltzmann constant, the relation t/°C = T/K − 273.15, the equality of Celsius and kelvin temperature intervals, and the tonne as an accepted non-SI unit at 10³ kg, adopted by the CIPM in 1879.

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