Metric vs Imperial

Metric, U.S. customary and British Imperial: three labels to distinguish

Metric uses decimal prefixes. U.S. customary and British Imperial units use specific relationships, and their liquid measures differ. Start with the complete unit name, choose the correct dimension, then convert with an exact factor or temperature relationship.

This guide includes an exact conversion chart, step-by-step examples, three diagrams and practice answers. Each linked example opens the relevant converter with its inputs already selected. The calculations use nominal values so you can reproduce them; the reporting guidance explains how actual measurement precision changes the final answer.

Prefixes are scale factors, not new physical quantities: $1\,\mathrm{km}=10^3\,\mathrm m$, $1\,\mathrm{cm}=10^{-2}\,\mathrm m$ and $1\,\mathrm{mm}=10^{-3}\,\mathrm m$. The prefix is part of the unit symbol. Time is a useful reminder that everyday units need not follow decimal steps: $1\,\mathrm h=60\,\mathrm{min}=3600\,\mathrm s$.

The kilogram is the base unit for mass, not the gram. Area and volume are derived quantities. For current SI terminology, see the BIPM SI Brochure, updated June 2026. Its current non-SI chapter lists the litre among historical names for decimal multiples and submultiples; older “accepted units” summaries use a different classification.

Exact metric and inch-pound conversion chart

These equalities are exact definitions or exact consequences of them. They apply to international length units and avoirdupois mass. An exact multiplier can still produce a repeating decimal when used in reverse; keep its full value through the calculation and round only the result you report.

Cross-check the conventions against NIST’s factor tables and the UK numerical definitions. Some source tables shorten decimal entries. Here the full pound factor, squared foot factor and liquid-volume factors are retained. A rounded table entry should not be relabeled as an exact definition.

A conversion method you can check line by line

1. Name the quantity and convention. Record length, area, volume, mass or a temperature reading or change. Keep “US liquid,” “Imperial,” “avoirdupois” and any historical qualifier with the original value.
2. Orient the factor so the old unit cancels. Multiply by a ratio equal to one. For reverse conversions, invert the factor rather than guessing whether the number should grow or shrink. Square or cube the length ratio when the quantity requires it.
3. Check magnitude and report precision. Preserve guard digits, compare against a rough estimate, then apply the precision required by the question or measurement. Reversing the conversion is a useful arithmetic check, although it cannot prove that you selected the intended convention.

Here $x_s$ and $x_t$ are the source and target numerical values, while $f_s$ and $f_t$ are their numerical factors to the same base unit. For example, use meter factors for length. The concrete cancellation lines below retain the units explicitly. Absolute temperatures require an affine relationship, so the simple multiplicative recipe needs an offset there.

A useful mental check is $1\,\mathrm{in}\approx2.5\,\mathrm{cm}$ or $1\,\mathrm{lb}\approx0.45\,\mathrm{kg}$. These are estimates, not the factors used for the exact examples. NIST’s guidance on rounding is linked in the sources. For recorded measurements, extra decimal places do not create extra instrument resolution.

Length example: feet and inches to meters

Suppose a nominal height is five feet and ten inches. Treat that as two lengths to add, not a decimal number written as $5.10\,\mathrm{ft}$. Use the international foot and inch, convert the feet into inches, then apply the exact meter factor. The result describes the same length using a different unit.

1. Convert the whole feet and add the remaining inches.$$5\,\mathrm{ft}\frac{12\,\mathrm{in}}{1\,\mathrm{ft}}+10\,\mathrm{in}=70\,\mathrm{in}$$
2. Cancel inches against the factor’s denominator.$$70\,\mathrm{in}\frac{0.0254\,\mathrm m}{1\,\mathrm{in}}=1.778\,\mathrm m$$
3. Check the reverse operation before rounding.$$1.778\,\mathrm m\frac{1\,\mathrm{in}}{0.0254\,\mathrm m}=70\,\mathrm{in}$$

Open the feet-and-inches exampleCheck the reverse conversion

The full nominal result is also $177.8\,\mathrm{cm}$. If the original height came from a tape marked only in whole inches, that decimal expansion would not establish millimeter measurement accuracy. Record the original reading and choose an output precision that fits its purpose. A decimal foot is a different input convention from a mixed feet-and-inches entry.

Area and volume: square or cube the whole length factor

A square foot is a square with sides of one foot, not one foot multiplied by a dimensionless number. Each side contributes a conversion factor. A cubic foot has three such dimensions. Starting with the international foot, the following identities explain why one linear multiplier is insufficient.

A rectangular room

For a nominal room measuring $12\,\mathrm{ft}$ by $10\,\mathrm{ft}$, first multiply the side lengths. Then convert the area with the squared ratio. Converting both sides to meters first gives the same answer, which supplies a second formulation for checking the result.

If the task requests two decimal places, report $A\approx11.15\,\mathrm{m^2}$. That is a reporting choice, not a new exact equality. Flooring quantities can also depend on layout and waste allowance, which this geometry example does not estimate. Use the Area Formulas guide when the boundary is not a rectangle.

A cubic foot in liters

The litre connects capacity to cubic length. Multiply the cubic-meter value by the exact liters-per-cubic-meter ratio. Do not cube the liter conversion again: the foot factor has already been cubed, and the last step simply changes volume units.

Open the cubic-foot volume conversion · Read Area Formulas

US liquid vs Imperial gallons, pints and fluid ounces

The US liquid gallon is defined as $231\,\mathrm{in^3}$ and contains $128$ US fluid ounces. The Imperial gallon is exactly $4.54609\,\mathrm L$ and contains $160$ Imperial fluid ounces. Combine these definitions with the exact inch factor to obtain the full decimal values below. The table covers liquid measures, not US dry measures or nutrition-labeling conventions.

Compare NIST’s US gallon definition with the UK capacity factors. The Imperial gallon and pint are larger, but the Imperial fluid ounce is smaller because the number of ounces per gallon differs. A fluid ounce is a volume; an unqualified avoirdupois ounce is a mass.

Two gallons, with the convention stated first

Take the same numerical count of gallons in each system. Choose the corresponding liter factor, multiply once, then keep the system label with the answer so another reader can reproduce the calculation.

Try two US liquid gallonsTry two Imperial gallonsCheck one US fluid ounceCheck one Imperial fluid ounce

For recipes, also identify the cup or spoon convention. A metric recipe cup and a US customary cup need not have the same volume. Converting a volume of flour into a mass requires an ingredient-density or packing assumption; changing unit systems does not supply that missing information. See Kitchen Conversions for those distinctions.

Mass example: avoirdupois pounds to kilograms

For a nominal mass of $10\,\mathrm{lb}$, select the avoirdupois pound used in ordinary mass measurements. It is divided into $16$ avoirdupois ounces. A troy ounce is a different unit, so precious-metal labels need an explicit convention. Pound-force is also a different quantity from pound mass.

1. Write the exact mass factor with kilograms in the numerator.$$m=10\,\mathrm{lb}\frac{0.45359237\,\mathrm{kg}}{1\,\mathrm{lb}}=4.5359237\,\mathrm{kg}$$
2. Check that a pound is less than a kilogram. For the same mass, the numerical kilogram value should therefore be smaller than the numerical pound value.
3. If the question requests three decimal places, report $m\approx4.536\,\mathrm{kg}$. Keep the original nominal result for the reverse check; do not multiply successive rounded answers and expect exact recovery.

Mass and volume are separate dimensions. Converting pounds into liters requires density, not another pounds-to-kilograms factor. Similarly, a specification using “ton” should say US short ton, Imperial long ton or metric tonne before a conversion begins. The weight and mass converter labels those choices separately.

Temperature readings use an offset; temperature changes do not

Let $c$ and $f$ be the numerical readings in degrees Celsius and Fahrenheit respectively. They are scale numbers, so the formulas below act on those numbers; attach the selected unit when stating the final temperature. The scales differ in both interval size and zero point. Kelvin uses the same interval size as Celsius but a different zero.

Convert a reading, then check it in reverse

For a reading of $68\,^\circ\mathrm F$, subtract the Fahrenheit offset first, then scale the remaining interval. This gives the Celsius reading. Applying the inverse formula restores the original number. The order matters: scaling first and subtracting the unscaled offset afterwards would give a different answer.

Convert the Fahrenheit readingCheck the Celsius reading in reverse

Convert a rise or fall

Subtract two scale readings and the shared offset cancels. Only the interval-size ratio remains. A signed difference can be negative for cooling; it is not an absolute temperature below a scale’s physical lower limit.

Thus a rise of $20\,^\circ\mathrm C$ corresponds to a rise of $36\,^\circ\mathrm F$. An absolute reading of $20\,^\circ\mathrm C$ instead corresponds to $68\,^\circ\mathrm F$. Our linked example deliberately selects difference mode. See the NIST temperature reference in the sources for the distinction.

Practice conversions with worked answers

Choose the convention and the quantity before opening each answer. The prefilled links retain the stated mixed-unit or difference mode. Try the arithmetic yourself, then use a reverse calculation or a second arrangement of the same factors to check it.

Metric vs imperial questions

Sources and calculation notes

Reviewed October 30, 2026. Definitions are checked against primary measurement references. The examples are original nominal calculations. The SVG figures use independently checked volume ratios, square-grid dimensions and affine temperature coordinates; they remain responsive illustrations rather than physical measuring instruments.

1. BIPM: SI Brochure, ninth edition, June 2026 update

   Current base units, decimal prefixes, and chapter four's treatment of non-SI units including the litre. Use this update for SI status rather than older guides.

2. NIST SP 1038: conversion factors for general use

   The 2006 reference identifies the US liquid gallon as 231 cubic inches and 128 US fluid ounces. Its rounded litre entry is expanded here from those definitions; it is not our source for current SI definitions.

3. NIST SP 811: alphabetical conversion factors

   A cross-check for length, mass, area and liquid-volume factors. Bold factors are exact; other displayed entries may be rounded.

4. NIST SP 811: using factors and rounding converted values

   Multiply in the stated direction, divide for the reverse direction, and retain appropriate precision when reporting a converted measurement.

5. UK Units of Measurement Regulations 1995: Schedule

   As-made numerical definitions for Imperial capacity and avoirdupois mass, including the gallon, pint, fluid ounce and pound. Cited for these factors, not for present-day trading or labeling rules.

6. NIST: SI units — temperature

   Celsius, Fahrenheit and kelvin conversions, with the distinction between a scale reading and a temperature interval.

7. NIST: U.S. survey foot and legacy records

   Explains the international foot and why historical survey-foot data still need their original unit definition.

Continue with the quantity you need

Use Length, Area, Volume, Mass or Temperature for another input. For a calculation record that keeps units and assumptions beside the result, read Engineering Notes on Graph Paper.