How to use the Percent Error Calculator
- Enter the accepted or theoretical value.
- Enter the value you measured.
- Read the percent error and the absolute error.
- Note the direction — a consistent bias points to a systematic problem, not random noise.
How the calculation works
Percent error divides the size of the discrepancy by the accepted value: |measured − accepted| ÷ |accepted| × 100. Using the accepted value as the base is what distinguishes percent error from percent difference, which divides by the mean of the two values and is used when neither is authoritative.
The distinction between accuracy and precision matters when interpreting the result. Percent error measures accuracy — how close you are to the truth. Repeatability across trials measures precision. A thermometer reading 2 °C high every time is precise but inaccurate, and only a calibration check reveals it. Random scatter reduces with repeat measurements and averaging; systematic bias does not, no matter how many trials you run.
In teaching labs, errors under about 5% are typically treated as acceptable for simple apparatus, though the meaningful threshold depends entirely on the instrument's stated tolerance.
Percent error = |measured − accepted| / |accepted| × 100Source: Standard error analysis conventions; NIST guidance on measurement uncertainty (NIST TN 1297).
Worked example
A pendulum experiment yields g = 9.65 m/s² against the accepted 9.81 m/s².
- Absolute error: |9.65 − 9.81| = 0.16.
- Divide by accepted: 0.16 ÷ 9.81 = 0.0163.
- Multiply by 100.
1.63% error — a good result for a stopwatch-timed pendulum, and biased low, consistent with timing lag.
Frequently asked questions
Should percent error be signed?+
The conventional figure is absolute, but keeping the sign tells you whether you are consistently over or under, which helps diagnose systematic bias.
What if there is no accepted value?+
Use percent difference, dividing by the mean of the two measurements instead.
Does a low percent error mean a good experiment?+
Not necessarily. Cancelling errors can flatter a poor method. Report uncertainty alongside the error figure.
What counts as an acceptable error?+
It depends on the instrument tolerance. Compare against the manufacturer's stated accuracy rather than a generic threshold.
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.