Percentage Error Formulas for Measurements
Percentage error formulas for engineers: absolute, relative and percentage error of a meter reading, with worked examples and a tolerance check.
The formulas
| To find | Formula |
|---|---|
| Error | error = measured − true |
| Absolute error | |error| = |measured − true| |
| Relative error | relative error = (measured − true) / |true| |
| Percentage error | percentage error = relative error × 100 |
| Absolute percentage error | |measured − true| / |true| × 100 |
The error is taken as a share of the true (reference) value, so the true value cannot be zero. A negative result means the reading is low and a positive one means it is high. Percentage error is not the same as percentage difference, which compares two values when neither is the reference.
Worked example: a voltmeter reading
A reference source is set to 230 V and a voltmeter reads 229.2 V.
- Error = 229.2 − 230 = -0.8 V
- Relative error = -0.8 / 230 = -0.003478
- Percentage error = -0.003478 × 100 = -0.3478%, so the meter reads low
- Against a ±0.5% tolerance the absolute percentage error of 0.3478% is within the limit
Worked example: a measured constant
A pendulum test gives g = 9.81 m/s² against the accepted 9.80665 m/s².
- Error = 9.81 − 9.80665 = 0.00335 m/s²
- Percentage error = 0.00335 / 9.80665 × 100 = 0.03416%
Frequently asked questions
Why divide by the true value and not the measured one?
The true value is the reference the reading is judged against. Dividing by the measured value would make the same error look different depending on the reading.
What does a negative percentage error mean?
The measured value is below the true value. A positive error means it is above. Use the absolute percentage error when only the size matters.
What if the true value is zero?
There is no percentage error, because any error is too large a share of zero to express. Use the absolute error instead.
How is this different from percentage difference?
Percentage error compares a value with a known true value. Percentage difference compares two values when neither is the reference, using their average as the base.
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