Measurement guide
How to convert measurements without inventing precision
Unit conversion changes how a quantity is expressed. It cannot improve the measurement that produced the quantity.
· About 7 minutes
Keep the physical dimension unchanged
A valid conversion expresses the same physical quantity in another unit. Length converts to length, area to area, and temperature to temperature. A conversion factor can be written as a fraction equal to one, with units arranged so the unwanted unit cancels.
Because one inch is exactly 2.54 centimeters, converting 12 inches to centimeters can be written as 12 in × 2.54 cm/in. The inch units cancel, leaving 30.48 centimeters. Writing units inside the arithmetic is a simple way to catch reversed factors.
Squared and cubed units need squared and cubed factors
A common mistake is applying a length factor directly to area. One foot equals 0.3048 meter, but one square foot is not 0.3048 square meter. A square has two dimensions, so the factor must be squared: 0.3048² = 0.09290304 square meter.
Volume uses the cube of a length factor. If every edge of a cube is converted, three factors are multiplied. This is why area and volume differences grow much faster than the underlying length conversion.
Some factors are exact and some inputs are measured
Modern definitions make many conversion factors exact. One inch is exactly 0.0254 meter, and one international foot is exactly 0.3048 meter. Using more digits for an exact factor reduces conversion error, but it does not remove uncertainty from a measured input.
If a board was measured only to the nearest centimeter, converting its length to inches and displaying eight decimal places does not reveal its true length more precisely. Those extra digits describe calculator arithmetic, not measurement certainty.
Round at the end
Keep adequate internal precision through intermediate steps and round the final result. Rounding after each step can accumulate error. The number of meaningful digits in the output should reflect the input data and the purpose of the result.
Significant figures are one convention for communicating measurement precision. Decimal places are not the same thing: 120.0 has four significant figures, while 0.012 has two. For practical work, state an appropriate tolerance when it matters more than a digit-count rule.
Temperature is an affine conversion
Most unit conversions multiply by a fixed factor. Celsius and Fahrenheit also have different zero points, so their conversion requires multiplication and addition. Celsius to Fahrenheit is °F = °C × 9/5 + 32. Temperature differences are different: a change of 1°C equals a change of 1.8°F, without adding 32.
Kelvin and Celsius use equal-size intervals, but zero kelvin is absolute zero, equal to −273.15°C. Kelvin values below zero are not physically valid in the ordinary thermodynamic scale.
Match the tool to the task
Use the Length Converter for one-dimensional units, the Area Converter for square units and land measures, and the Temperature Converter for affine temperature scales. For engineering, surveying, laboratory, legal, or regulated work, confirm the required unit definition, tolerance, rounding rule, and calibration standard.
Conversion preserves a quantity only when the original unit, dimension, definition, and measurement are understood correctly. More displayed digits do not create more reliable data.