Unit Conversion Chart: Exact Factors for All 18 Categories

1. How to Read This Chart

Most conversion charts list pairs: inches to centimetres here, pounds to kilograms there. That format breaks down the moment you need a pair nobody thought to print. This chart instead gives one row per unit, expressed in the base unit of its category, so any pair inside a category can be built by dividing two rows.

Each row has four fields. Unit names the unit and its symbol in brackets; when a unit has variants, the variant is part of the name, so there is never an ambiguous "gallon" or "ton" in the tables. 1 base unit is the value of one of that unit, expressed in the category's base unit. Basis is either exact, meaning the number is fixed by a definition and carries no uncertainty, or convention, meaning it was adopted by agreement and could in principle have been chosen differently. Source names the standard the number comes from.

Digits are not rationed. Where a factor terminates, the full decimal is printed, so 1 pound shows as 0.45359237 kg rather than 0.4536. Where a factor is a ratio that never terminates, such as the torr at 101325/760 pascal, the fraction itself is printed alongside a fifteen-figure decimal. Nothing on this page is rounded to four digits to look tidy, because a rounded factor is indistinguishable from a correct one until the error is large enough to be expensive.

The factors are definitions, not measurements, so they impose no precision limit of their own. If you measured a length to three significant figures, your converted answer has three significant figures, however many digits the definition behind it carries. For the method that turns these factors into an answer, and for the conversion families where a factor does not exist at all, see the How to Convert Units guide.

2. Quick Conversions

These are the pairs people look up most, both directions, carried to the full precision of the definition underneath them.

3. The Chart, Category by Category

Every category is rendered in its own base unit. Energy and power share one category on this site and are shown as two tables, because a joule and a watt are not the same kind of quantity.

Length

All imperial length units descend from one sentence in the 1959 agreement: 1 yard = 0.9144 m exactly. Everything else in this table is that number multiplied or divided.

Area

Area factors are length factors squared, which is why 1 m² is 10.7639 ft² and not 3.28084 ft². The acre is a chain-and-furlong artefact: 1 acre = 4,840 square yards exactly.

Volume and cooking

There is no single gallon. The US gallon is 231 cubic inches by statute; the imperial gallon is 4.54609 L. Every US cooking measure below is an exact subdivision of the US gallon, not an independently defined spoon.

Weight and mass

The pound was fixed at 0.45359237 kg by the same 1959 agreement, and the kilogram itself was redefined in 2019 in terms of the Planck constant. The ounce is 1/16 of a pound — avoirdupois, not troy.

Time

Only one entry here is a convention rather than a definition. The month has no fixed length, so the mean Julian month — one twelfth of a 365.25-day Julian year — is what this site uses.

Pressure

Torr and millimetre of mercury are two different units that are usually treated as one. The torr is exactly 1/760 atm; the conventional millimetre of mercury is a separate adopted value. They differ in the seventh significant figure.

Force

A pound-force is the weight of one avoirdupois pound under standard gravity, so its exact value depends on the adopted value of g — 9.80665 m/s² exactly.

Torque

Torque shares the pound-force definition with force, so the foot-pound is exactly 1 lbf × 1 ft. Torque and energy have the same dimensions but are not interchangeable.

Energy

The BTU and the calorie both have several mutually incompatible definitions. The values below are the IT BTU and the thermochemical calorie, which is what this site uses throughout.

Power

Mechanical horsepower is exactly 550 foot-pounds-force per second, which is why its decimal runs to sixteen digits. Metric horsepower is a different unit (75 kgf·m/s) and is about 1.4% smaller.

Frequency

Hertz is cycles per second. The only non-terminating entry is rpm, because a minute is not a power of ten — 1 rpm = 1/60 Hz exactly.

Speed

Speed is a compound unit, so each factor is a length factor divided by a time factor. The knot is one nautical mile per hour and is exactly 463/900 m/s.

Density

Density is mass over volume, so it carries a cubed length factor. Note that 1 g/cm³ and 1 kg/L are the same number in different clothes, both exactly 1,000 kg/m³.

Flow rate

Flow rate is volume over time. CFM and gpm are 60-second units, which is where the factor of 60 enters every imperial flow conversion.

Data storage

Storage and data rate are different things measured with confusable names. Here 1 KB is 1,024 bytes, following the binary convention this site uses throughout; a decimal kilobyte is 1,000 bytes.

Angle

The base unit of angle is the radian, and the degree is defined as an exact fraction of it — π/180. Because π is irrational, no decimal expansion of a degree is exact, and any chart that prints one to six digits has already rounded it.

Temperature

Temperature is the one everyday quantity where the conversion is not a multiplication. Celsius and Fahrenheit have different zero points, so the relationship is affine: a factor plus an offset. Kelvin shares the Celsius step size exactly, so that pair needs addition and no multiplication. Temperature therefore has no rows in the tables above, and the absence is the point.

Fuel economy

Fuel economy is the other everyday conversion that is not a multiplication. Miles per gallon is distance divided by volume; litres per 100 kilometres is volume divided by distance. The two are reciprocal, so a fixed improvement in one is not a fixed improvement in the other, and a chart that lists a single factor for the pair is quietly wrong at both ends of its range.

Electric

The electrical category is where a factor-based chart breaks down most often, because it contains five different kinds of relationship and only one of them is a single multiplication. These are deliberately absent from the tables above.

4. Which Factors Are Exact, and Which Are Conventions

In a conversion chart, "exact" has a narrow meaning. It does not mean "accurate to many digits" — it means the number is fixed by a definition and has no uncertainty whatsoever. A factor can be exact and still be a poor choice; and a factor can carry ten digits and still be an approximation. Of the 101 factors on this page, 99 are exact and 2 are conventions.

4.1 One sentence defines most of the imperial system

The 1959 International Yard and Pound Agreement fixed two numbers: 1 yard = 0.9144 metre and 1 pound = 0.45359237 kilogram, both exact. Every imperial length, area, volume and mass factor on this page is a descendant of one of those two sentences. Nothing else needed to be defined.

This is why the chart can print thirteen digits for a pound and still claim the number is exact. The definition is not a measurement of a physical object that might drift; it is a stipulated equivalence, and the only thing that limits how many digits you may use is the precision of the quantity you started with.

4.2 Metric factors are exact by construction

Decimal prefixes carry no uncertainty at all, because they are powers of ten applied to a base unit. Since 2019 the base units themselves are defined through fixed constants: the kilogram through the Planck constant, the metre through the speed of light, the second through the caesium hyperfine frequency. There is no longer a platinum cylinder in a vault whose mass is a measured quantity, so a metric factor is exact rather than merely known to nine digits.

4.3 The conventions

Two entries in the chart are marked convention rather than exact, and both are worth understanding because they appear in real work.

The month has no fixed length. It is 28, 29, 30 or 31 days depending on which month you mean. Any chart that prints a single number for it has chosen a convention, and this site uses the mean Julian month, one twelfth of a 365.25-day Julian year, which is 30.4375 days. Converting a monthly rate to a daily one through that number gives an average, not a calendar answer.

The conventional millimetre of mercury is a defined value, 133.322387415 pascal, adopted for the sake of consistency rather than derived from first principles. It is not the same unit as the torr, which is exactly 1/760 of a standard atmosphere. The two differ in the seventh significant figure, which is enough to matter in vacuum metrology and nowhere else — but they are two units, and a chart that lists one number for both is wrong about one of them.

5. Where One Name Means Several Numbers

The most expensive conversion errors are not arithmetic errors. They occur when a unit name silently covers more than one quantity and the reader assumes the one they meant. The table below lists every unit on this site that has variants, with the spread between the smallest and the largest.

The pattern is that the spread is almost always larger than the precision anyone brings to the problem. Choosing the wrong ton costs 12 per cent; choosing the wrong gallon costs 20 per cent; confusing a metric and an imperial tablespoon costs 35 per cent. None of those errors announce themselves, because every one of them produces a plausible number. See the unit conversion mistakes hub for what happens when one gets through review.

6. Conversions That Are Not a Single Multiplication

Three families in this chart do not reduce to a factor, and they are the reason the tables above have gaps in them. Temperature is affine: Celsius and Fahrenheit differ by an offset as well as a scale. Fuel economy is reciprocal: miles per gallon and litres per 100 km run in opposite directions. Electric quantities need a third value — a voltage, a power factor or a system voltage — before any conversion can be attempted. The individual sections above give the formulas; the How to Convert Units guide explains why multiplication fails for each of them and what to do instead.

7. Printing and Using This Chart Offline

Every table here is plain HTML, so your browser's print function renders it directly — there is no PDF to download and no image to zoom into. The site's print stylesheet strips the navigation and footer so the tables begin at the top of the page, and table rows are set not to break across pages.

For a desk copy, print in landscape and set the scale to fit the width of the page; the widest tables have four columns and will fit comfortably on A4 or Letter. If you only need one category, print that section on its own — each is anchored, and the jump list at the start of Section 3 links straight to it.

One caution about offline use: the factors here are definitions, so they will not go stale, but the package this page was printed from carries a date. If a national metrology institute revises a convention — as the kilogram definition changed in 2019 — this page will be updated and the offline copy will not be. The methodology page explains how revisions are tracked and how to check a value against its source.

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