Relative Error Calculator
Enter your measured (approximate) value and the true (accepted) value to get the relative error as a decimal, the percent error, and the absolute error, with the formula shown.
Example: with Measured (approximate) value 49.5 · True (accepted) value 50 → Relative error: 0.01.
- Percent error1%
- Absolute error0.5
Computed by the calculator below using its default values. Change any input to see your own numbers.
Relative error = |measured - true| / |true|; percent error is that same number times 100.
Absolute error, made relative
Absolute error is just the gap between what you measured and the true value: |measured - true|. On its own it lacks context, since being off by 1 is trivial when measuring a mile and catastrophic when measuring a millimeter. Relative error fixes that by dividing the gap by the size of the true value, so the answer scales with what you are measuring.
Relative, percent, same idea
Relative error is a bare ratio, like 0.02. Multiply by 100 and it becomes percent error, 2%, the identical information in friendlier clothes. Some fields keep a sign to show direction, measured too high or too low; this calculator reports the magnitude, which is what relative error usually means in a lab or textbook. Pair it with significant figures and you have an honest statement of measurement quality.
How it’s calculated
Relative error = |measured - true| / |true|. Percent error is the same quantity times 100. Absolute error is |measured - true|. The true (accepted or exact) value goes in the denominator; when it is zero, relative error is undefined.
Uses the magnitude (absolute value) of the difference, so results are non-negative and do not indicate whether the measurement was high or low.
Relative vs percent error, worked
| Measured | True | Relative | Percent |
|---|---|---|---|
| 49.5 | 50 | 0.01 | 1% |
| 105 | 100 | 0.05 | 5% |
| 9.7 | 9.81 | 0.0112 | 1.12% |
| 2.54 | 2.5 | 0.016 | 1.6% |
Computed as |measured - true| / |true|; the percent column is that ratio times 100.
Common mistakes
- Dividing by the measured value instead of the true value. The accepted value belongs in the denominator.
- Reporting relative error and percent error as if they were separate checks; percent error is just relative error times 100.
- Trying to compute relative error against a true value of zero, where the ratio blows up and is undefined.
Frequently asked questions
What is the relative error formula?
Relative error = |measured - true| / |true|. It expresses the absolute error as a fraction of the true value, so multiply by 100 to get percent error.
What is the difference between relative and percent error?
None mathematically. Percent error is relative error multiplied by 100, so a relative error of 0.05 is the same as 5% error.
Is relative error the same as absolute error?
No. Absolute error is the raw gap |measured - true|. Relative error divides that gap by the true value, turning it into a scale-free ratio you can compare across different measurements.
Why does the true value go in the denominator?
Because you are asking how big the error is compared with the correct answer. Using the accepted value as the reference keeps results consistent and comparable.
What if the true value is zero?
Relative and percent error are undefined, since dividing by zero has no meaning. Report the absolute error instead, or choose a nonzero reference appropriate to the problem.