Use a factor that cancels the starting unit
Write the starting number with its unit, then multiply by a ratio equal to one. Place the unwanted unit opposite the starting unit so it cancels, leaving the desired unit. This dimensional-analysis approach makes a reversed factor easier to spot.
Some stated factors are exact definitions, while measured inputs are not exact. Keep extra digits during the calculation and round the final result according to the precision needed for the decision.
Worked example: feet to metres
Convert a measured length of 14 feet to metres using the exact relationship 1 foot = 0.3048 metre. The measurement itself is shown only to the nearest foot, so displaying many final decimal places would imply more measurement precision than provided.
Area, volume, and temperature need special care
When converting area, square the linear factor; when converting volume, cube it. Since 1 foot equals 0.3048 metre, 1 square foot equals 0.3048², or 0.09290304 square metre. Applying the linear factor once to an area is a common and substantial error.
Temperature scales use an offset as well as a multiplier, so they are not converted by a simple ratio around their zero points. For example, °F = °C × 9 ÷ 5 + 32, while °C = (°F − 32) × 5 ÷ 9. Apply operations in the written order.
Check direction, magnitude, and rounding
Before accepting a result, ask whether the number should become larger or smaller. Converting metres to centimetres produces a larger numerical value; converting centimetres to metres produces a smaller one. A rough mental estimate can expose a factor used backward or a misplaced decimal.
Do not mix mass and force, or weight and volume, without additional information. Converting a volume of an ingredient or construction material to mass requires its density, which can vary with composition, packing, moisture, or temperature.
Assumptions and limitations
Assumptions used in the explanations
- The source and target units describe the same kind of quantity.
- The selected conversion factor is applicable and is oriented so source units cancel.
- Intermediate calculations retain sufficient precision before final rounding.
What this guide cannot tell you
- A unit conversion cannot supply missing density, concentration, exchange-rate, or material-property information.
- Rounded or measured inputs limit meaningful precision even when a conversion factor is exact.
- Specialized technical work may require specified constants, reference conditions, tolerances, or domain conventions.
This guide provides general educational information, not financial, tax, legal, or lending advice.
Frequently asked questions
How do I know whether to multiply or divide?
Write the factor as a fraction and orient it so the starting unit cancels. Multiplication by that labeled fraction handles the direction without relying on memory.
Why can’t I use a length factor directly for square units?
Area has two dimensions, so both are converted. The linear factor must be squared; for volume, it must be cubed.
Why do temperature conversions add or subtract a number?
Common temperature scales have different interval sizes and different zero points. The offset aligns the zero points, while the multiplier converts the interval size.
How many decimal places should a conversion show?
Keep guard digits during the calculation, then round for the accuracy of the source measurement and the decision. Extra displayed digits do not make an imprecise measurement more accurate.