Percentage error calculator

• Gravity: a pendulum experiment gives $g = 9.6$ m/s² against an accepted 9.8 m/s². $|9.6 - 9.8| \div 9.8 \times 100 = 2.04\%$ (low).
• Specific heat capacity: you measure 1,050 J/kg °C for aluminium, accepted 900. $150 \div 900 \times 100 = 16.7\%$ (high).
• Boiling point: water boils at 98 °C in your experiment, accepted 100 °C. $2 \div 100 \times 100 = 2\%$ (low).

Percentage error compares your result with a known true value. Percentage uncertainty describes the range of a single measurement, without needing a true value: a reading of 20.0 cm ± 0.1 cm has an uncertainty of $0.1 \div 20 \times 100 = 0.5\%$. A good experiment has a small percentage error that sits inside its uncertainty.

• Systematic errors push every reading the same way: a zero error on a balance, or energy lost to the surroundings in a heating experiment (which is why measured specific heat capacities usually come out high). Repeating doesn't remove them.
• Random errors scatter readings either side of the true value: reaction time with a stopwatch, or reading a scale. Repeating and averaging reduces their effect.

State the percentage error, say whether the result is high or low, and give the most likely cause in that direction. "My value of $g$ was 2% low, probably because air resistance slowed the pendulum" earns more credit than "human error". Then suggest a specific improvement, such as using light gates instead of a stopwatch.

Percentage error questions often follow a calculation from a practical: the specific heat capacity calculator, the spring constant calculator or the density calculator. For percentage change between any two numbers, use our percentage calculator.

• Accurate: close to the true value (small percentage error).
• Precise: repeat readings are close to each other (small spread), even if they're all wrong.
• Repeatable: you get similar results when you repeat it; reproducible: someone else with different equipment gets similar results.

A thermometer that always reads 2 °C high is precise but not accurate; that's a systematic error, which shows up as a consistent percentage error in one direction.