Unit conversion done properly

Unit conversion looks like the most mechanical thing in this collection, and mostly it is. The interesting part is the small set of cases where a multiplication is not enough: temperature needs an offset, pressure needs a reference, and several unit names refer to more than one quantity.

Imperial units are defined in metric

Since the international yard and pound agreement of 1959, the inch is exactly 25.4 millimetres and the pound is exactly 0.45359237 kilograms. Not approximately — by definition. Every derived unit follows: a foot is exactly 0.3048 m, a mile exactly 1609.344 m.

So every metric-to-imperial conversion of length or mass is exact, and any residual error comes from rounding in your own arithmetic rather than from the units. The factor 2.54 centimetres per inch is not an approximation of a messy physical relationship; it is the definition.

Rounding matters where error accumulates or tolerance is tight. Using 2.5 centimetres per inch is a 1.6 percent error: across 40 cabinet units nominally 24 inches wide, that is over a foot of accumulated shortfall. A machining tolerance of plus or minus 0.001 inch is 0.0254 mm, so any rounding consumes a meaningful share of the budget before the machine starts. Convert once at full precision rather than repeatedly through a chain of drawings.

One historical footnote that still causes trouble: the United States retained a separate survey foot of 1200/3937 metres for land surveying, differing from the international foot by about two parts per million. Negligible across a room, metres across a state plane coordinate baseline. It was deprecated at the end of 2022 but persists in older datums and records.

Nominal sizes are names, not measurements

A great many stated dimensions were never measurements, so no conversion will make them correct.

A nominal two-by-four measures 1.5 by 3.5 inches after drying and planing. A one-by-six is 0.75 by 5.5. Nominal pipe size is a designation whose relationship to physical dimensions varies with schedule — a 2-inch pipe has a 2.375 inch outside diameter. Screen sizes are diagonals. Small drill bits are named by gauge or letter.

The rule is to convert measured dimensions and look up nominal ones. Converting 2 inches to 50.8 mm for a two-by-four answers the wrong question precisely.

Mixed-unit projects have a related problem: metric sheet goods and imperial framing do not align. A 1220 by 2440 mm plywood sheet is about 48.03 by 96.06 inches, which is enough to matter when sheets are meant to butt on a stud layout.

Three tons and two ounces

Mass has two unit names that each refer to more than one quantity, and both differ by around 10 percent — enough to matter and small enough to survive a plausibility check.

The short ton used in the United States is 2,000 pounds or about 907 kg. The long ton is 2,240 pounds or about 1,016 kg. The metric tonne is 1,000 kg or about 2,205 pounds. A load specified in the wrong ton is roughly 10 percent out, which on a structural or shipping calculation is not a rounding error.

Ounces split by trade. An avoirdupois ounce is about 28.35 grams and is used for shipping, food, and general commerce. A troy ounce is about 31.10 grams — roughly 10 percent heavier — and is used for precious metals. But a troy pound is only 12 troy ounces against 16 avoirdupois, so a troy pound is lighter at about 373 grams versus 454. A gold price quoted per ounce is per troy ounce, and converting it with 28.35 overstates the per-gram price by about 10 percent.

A related trap is the fluid ounce, which measures volume and is not interchangeable with the ounce despite the name. Eight fluid ounces of water weighs about 8.3 ounces, of honey about 12, and of flour about 4.4. The United States and imperial fluid ounces also differ by about 4 percent, so British and American recipes do not share the unit.

Temperature needs an offset, and differences do not

Length and mass are ratio scales — zero means none of the quantity — so conversion is one multiplication. Celsius and Fahrenheit are interval scales with arbitrary zeros, so conversion needs a factor and an offset: multiply by 9/5 and add 32.

Kelvin is a ratio scale, with zero at absolute zero, and shares the Celsius degree size. So Celsius to Kelvin needs only the offset of 273.15. This is why physics uses Kelvin: doubling a Kelvin temperature genuinely doubles average molecular kinetic energy, while doubling a Celsius figure means nothing physical.

The error worth internalising is that converting a temperature difference uses the factor and not the offset. A 10 °C rise is an 18 °F rise, not 50 °F. This appears constantly in specifications: a thermal expansion coefficient per °C converts to per °F by dividing by 1.8; a thermostat differential of 2 °C is 3.6 °F; an accuracy of ±0.5 °C is ±0.9 °F. Applying the 32-degree offset to any of these is wrong by an enormous margin, and because the result still looks like a temperature it can survive review.

A useful check: a difference in Celsius and the same difference in Kelvin are numerically identical, since the degree size is the same. And −40 is the single point where Celsius and Fahrenheit agree, which makes a good test of any conversion routine.

Pressure needs a reference

Pressure conversions are simple multiplications, but the number carries information no conversion can supply: what it is measured relative to.

A gauge reads the difference between system pressure and atmosphere. Absolute pressure is measured from vacuum. They differ by one atmosphere, about 14.7 PSI or 101.325 kPa, which is not a small gap. Every tyre gauge and compressor reads gauge; a tyre at 32 PSI gauge is at about 46.7 PSI absolute.

The distinction matters in three places. Thermodynamic calculations — gas laws, compressor work, steam properties — require absolute pressure, and gauge values give answers wrong by a factor at low pressures. Vacuum work must be absolute, since gauge pressure below atmosphere is negative. And weather and aviation pressures are absolute, so a barometric reading and a tyre gauge are not comparable.

Useful anchors: 1 bar is about 14.5 PSI and 1 atmosphere about 14.7, so the two are interchangeable to within 1.3 percent for rough work. 1 MPa is about 145 PSI. For water, roughly 1 PSI per 2.31 feet of head, or 9.8 kPa per metre — which is why tall buildings need booster pumps.

One temperature interaction worth knowing: gas pressure in a fixed volume rises with absolute temperature, roughly 1 PSI per 10 °F. A tyre set to 32 PSI on a 70 °F afternoon reads about 28 on a 30 °F morning, which is why manufacturer figures specify cold pressure.

Frequently asked questions

Calculators referenced in this guide