Percentage Error Calculator
Calculate percentage error from observed and true values with the formula |observed − true| ÷ |true| × 100. See absolute and relative error instantly.
About the Percentage Error Calculator
Percentage error measures how far a measured or observed value strays from the true or accepted value, as a share of that true value. This free percentage error calculator applies the standard formula: percentage error = |observed − true| ÷ |true| × 100. Enter both values and you instantly get the absolute error, the relative error as a decimal, and the percentage error, with the substituted formula shown so you can follow the working.
For example, if you measure gravitational acceleration as 9.7 m/s² when the accepted value is 9.81 m/s², the absolute error is 0.11, and the percentage error is 0.11 ÷ 9.81 × 100 = 1.12%. Physics and chemistry students use this after every lab experiment, and the same calculation checks forecasting accuracy, sensor calibration, quality-control tolerances and estimation exercises in engineering.
The calculator uses absolute values by convention, so the result is always positive regardless of whether you overshot or undershot. Everything computes live in your browser with no signup.
How to Use the Percentage Error Calculator
- 1Enter the observed (measured or estimated) value.
- 2Enter the true or accepted value.
- 3Read the absolute error, relative error and percentage error instantly.
- 4Check the substituted formula line to see the working.
Frequently Asked Questions
How do I calculate percentage error with an example?
Subtract the true value from the observed value, take the absolute value, divide by the absolute true value and multiply by 100. Measuring 9.7 against an accepted 9.81 gives |9.7 − 9.81| ÷ 9.81 × 100 = 0.11 ÷ 9.81 × 100 = 1.12%.
What is the difference between absolute, relative and percentage error?
Absolute error is the raw gap: |observed − true|. Relative error divides that by the true value, giving a unitless decimal. Percentage error is simply the relative error times 100. For observed 48 vs true 50: absolute error 2, relative error 0.04, percentage error 4%.
Can percentage error be negative?
By the standard convention, no — the formula uses absolute values, so 4% error means the same whether you measured too high or too low. Some teachers ask for signed error to show direction; in that case drop the absolute value and a negative result means you measured below the true value.
Why is percentage error undefined when the true value is zero?
Because the formula divides by the true value, and division by zero is undefined. If the accepted value is 0, use absolute error instead, or compare against the measurement range. The calculator flags this case rather than showing a misleading number.
What is an acceptable percentage error in a lab experiment?
It depends on the equipment and field. School physics labs often accept under 5–10%, undergraduate chemistry titrations aim for under 1–2%, and industrial calibration may require under 0.1%. Always compare your error against the tolerance your course or standard specifies.