Relative Error Calculator — Percent Error
Find the relative error (as a fraction) and percent error between an experimental or measured value and its accepted true value — the essential check on how accurate a measurement is.
Excellent
- 1
Absolute error
|9.8 − 9.81| = 0.01The raw magnitude of the discrepancy between your measurement and the accepted value. - 2
Relative error (ratio)
0.01 ÷ |9.81| = 0.001019 - 3
Percent error
0.001019 × 100 = 0.102
How does this calculator work?
Relative error is |measured − true| divided by |true|, giving a dimensionless fraction. Multiply by 100 for percent error. Values under 1 % are excellent, 1–5 % good, and above 10 % suggest a systematic problem. The result is undefined when the true value is zero.
Formula
How this is calculated
When you take a measurement or run an experiment, your result rarely matches the accepted value exactly. Relative error tells you how large that discrepancy is in proportion to the true value, making results from experiments of different scales comparable.
The absolute error is simply the magnitude of the difference: |measured − true|. Relative error divides that by the magnitude of the true value, giving a dimensionless fraction. Multiplying by 100 converts it to the familiar percent error. For example, measuring 9.80 m/s² for gravitational acceleration against the accepted value of 9.81 m/s² gives a relative error of 0.0010 (or 0.10 %).
Relative error is undefined when the true value is zero, since dividing by zero yields no finite result; use absolute error alone in that case. Precision (reproducibility) is a separate concept — a measurement can have low percent error by luck while remaining imprecise, and vice versa. Error bands of less than 1 % are generally considered excellent in introductory laboratory work, with 1–5 % good, 5–10 % acceptable, and above 10 % indicative of a systematic error or poor experimental technique.
Frequently asked questions
Absolute error is the raw magnitude of the discrepancy (|measured − true|) in the same units as the measurement. Relative error divides this by the true value, giving a dimensionless fraction that is comparable across different scales.
It depends on the field and instrument precision. As a rough guide: under 1 % is excellent, 1–5 % is good, 5–10 % is acceptable for many introductory labs, and above 10 % usually signals a systematic error worth investigating.
This calculator reports percent error as a positive magnitude (using absolute value). Some definitions keep the sign to show whether the measurement is above or below the true value — that signed version is simply (measured − true) / |true| × 100.
Also known as
TG we-Calculate Editorial Team. (2026). Relative Error Calculator — Percent Error [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/relative-error-calculator
TG we-Calculate Editorial Team. "Relative Error Calculator — Percent Error." TG we-Calculate. 2026. https://we-calculate.com/calculator/relative-error-calculator.
TG we-Calculate Editorial Team, "Relative Error Calculator — Percent Error," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/relative-error-calculator
@misc{wecalculate_relative_error_calculator, title = {Relative Error Calculator — Percent Error}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/relative-error-calculator}}, year = {2026}, note = {TG we-Calculate} }
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