Find relative error — how far a measured value is from a true (or accepted) value, as a percentage of that true value.
How it works
The formula is relative error = |measured − true| ÷ |true| × 100. A measurement of 9.8 against a true value of 10 has a 2% relative error.
What this does not include
This reports relative error as a positive percentage (using an absolute value), not signed error, which would indicate whether the measurement was too high or too low.
How to use this calculator
- Enter the measured value.
- Enter the true (or accepted/reference) value.
A worked example
A measured value of 9.8 against a true value of 10: relative error = |9.8−10|/10 × 100 = 2%.
A measured value of 105 against a true value of 100: relative error = 5%.
What the variables mean
| Variable | Meaning |
|---|---|
| Measured value | The observed or experimental value |
| True value | The accepted or actual value |
Edge cases worth knowing
Relative error is scaled by the true value, unlike absolute error. A 2-unit error means something very different measuring a value near 10 versus a value near 10,000 — relative error puts both on a comparable percentage scale.
A true value of zero makes relative error undefined — there’s no meaningful baseline to divide the error by, so the calculator declines to show a result.
Why use relative error instead of absolute error?
Absolute error (the raw difference) doesn’t account for scale — being off by 1 unit matters a lot when measuring something around 10, but barely at all when measuring something around 10,000. Relative error normalizes for that.
Why must the true value be nonzero?
Dividing by a true value of zero is undefined — relative error simply has no meaning when the reference value itself is zero.
Is relative error the same as percent error?
Yes — “percent error” is just relative error expressed as a percentage, exactly what this calculator returns.
