worldofcalcsPercentage Error Calculator
Percentage error
5%
Absolute error
5
Relative error
0.05
|105 − 100| ÷ |100| × 100 = 5 ÷ 100 × 100 = 5%
What is percentage error?
Percentage error compares a measured value with the true or accepted value: how far off it is as a percentage of the true value. Percentage difference compares two measurements when neither is the true value. For repeated readings, as in the Class 11 physics chapter on units and measurement, the mean is the best estimate and the mean absolute error gives its uncertainty.
Error formulas
Percentage error = |measured − true| ÷ |true| × 100 · Percentage difference = |a − b| ÷ ((a + b)/2) × 100 · Mean absolute error = Σ|aᵢ − ā| ÷ n
The relative error is the absolute error divided by the true (or mean) value; multiplying by 100 gives the percentage error. The result of repeated readings is written as ā ± mean absolute error.
Good to know
- Percentage error is always positive because it uses the absolute difference. Keep the sign if you need to know whether you measured too high or too low.
- Use percentage error when you know the true value, and percentage difference when comparing two measurements.
- Taking more readings and averaging them reduces random error, but not a systematic error such as a wrongly calibrated instrument.
- Round the mean absolute error to one or two significant figures, and the mean to the same decimal place.
- In sums and differences, absolute errors add; in products and quotients, percentage errors add.
Worked example: timing a pendulum
- Five readings of a pendulum's period: 2.63, 2.56, 2.42, 2.71 and 2.80 s
- Mean: (2.63 + 2.56 + 2.42 + 2.71 + 2.80) ÷ 5 = 2.624 s
- Absolute errors: 0.006, 0.064, 0.204, 0.086 and 0.176 s
- Mean absolute error: 0.536 ÷ 5 = 0.1072 s
- Relative error 0.1072 ÷ 2.624 ≈ 0.0409, so the percentage error is about 4.09%; period = 2.62 ± 0.11 s
Readings in the example
Each pendulum reading and its absolute error from the mean of 2.624 s.
| Reading | Value (s) | |aᵢ − ā| (s) |
|---|---|---|
| 1 | 2.63 | 0.006 |
| 2 | 2.56 | 0.064 |
| 3 | 2.42 | 0.204 |
| 4 | 2.71 | 0.086 |
| 5 | 2.80 | 0.176 |
Mean absolute error = 0.1072 s.