How to use
- Enter your measured (experimental) value.
- Enter the true (accepted or theoretical) value.
- Read the percent error, whether your result was above or below, and the absolute and relative error.
Percent error formula
Percent error = |measured − true| ÷ |true| × 100
- Absolute error is the gap, |measured − true|, in the measurement’s own units.
- Relative error is that gap divided by the size of the true value.
- Percent error is the relative error times 100.
- Signed percent error keeps the direction: (measured − true) ÷ |true| × 100. Negative means your result was too low.
The true value is always the one you divide by, so it can’t be 0.
Examples
- A 62-inch ladder measured as 63 inches: |63 − 62| ÷ 62 × 100 = 1.6129% above.
- Cardboard 8 inches long, measured as 8.25: 0.25 ÷ 8 × 100 = 3.125% above. The gap is smaller than the ladder’s, but the percentage is larger.
- Speed of sound measured as 329 m/s against 343 m/s: 14 ÷ 343 × 100 = 4.08163% below.
| Measured | True | Percent error | Signed |
|---|---|---|---|
| 63 | 62 | 1.6129% | +1.6129% |
| 62 | 63 | 1.5873% | −1.5873% |
| 101.5 | 100 | 1.5% | +1.5% |
| −9.5 | −10 | 5% | +5% |
Swapping the two values changes the answer, as the first two rows show.
Negative values, zero and naming
The calculator divides by |true|, so a positive signed error always means “above the true value”, even for negative quantities such as −10 °C.
When the true value is 0, percent error is undefined; report the absolute error instead. Note that NIST uses “error” for the signed difference, measured − true, and “absolute value of error” for its size.
What counts as an acceptable percent error depends on your field and instrument.
For a plain percentage change between two values, use the percentage calculator.