Percentage Error Calculator

Percentage Error Guide

The Formula

Percentage error = |measured − true| / |true| × 100. The absolute value (vertical bars) ensures the result is always positive when reporting error magnitude. The signed version (without absolute value) indicates whether the measurement was too high (+) or too low (−). Example: measuring 9.8 m/s² for gravitational acceleration when the true value is 9.81 m/s²: error = |9.8 − 9.81| / 9.81 × 100 = 0.102%.

Percentage Error vs Percentage Difference

Percentage error compares a measurement to a known true value (e.g., an accepted physical constant). Percentage difference compares two values without a known true value — neither is the 'correct' baseline. For two unknown values A and B: difference = |A−B| / ((A+B)/2) × 100. Use percentage error in experimental science; use percentage difference when comparing two estimates or measurements of equal standing.

Acceptable Error Ranges

Acceptable percentage error depends on the context and measurement method. In school physics experiments: under 5% is generally acceptable, 5–10% requires explanation, over 10% suggests systematic error or procedural mistake. Clinical measurements: blood pressure ±2%, blood glucose ±5–15% depending on meter. Manufacturing: often under 1% for precision components. Statistical surveys: ±3% for political polls (1000 sample size). The acceptable range is always context-dependent.

Sources of Error

Random errors cause scatter around the true value and can be reduced by taking multiple measurements and averaging. Systematic errors shift all measurements consistently in one direction (e.g., a miscalibrated instrument always reads 2% high). Percentage error primarily captures systematic error. Human error (parallax when reading a scale, reaction time), instrument precision, environmental factors (temperature affecting measurements), and approximations in calculation all contribute to percenta