🎯 Percent Error Calculator
Compare a measured value with the accepted true value to find the percent error, absolute error and relative error.
Quick answer: Percent error = |measured − true| ÷ |true| × 100. Measuring g as 9.6 m/s² when the true value is 9.81 m/s² gives 0.21 ÷ 9.81 × 100 ≈ 2.14% error.
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Percent Error Calculator inputs
Result
Percent error
2.14%
The measured value is 2.14% below the true value.
- Absolute error
- 0.21
- Relative error
- 0.021407
- Signed error
- −2.1407%
Step by step
- Absolute error: |9.6 − 9.81| = 0.21
- Divide by the true value: 0.21 ÷ |9.81| = 0.021407
- Multiply by 100: 0.021407 × 100 = 2.1407% ≈ 2.14%
The percent error formula
Percent error tells you how far an experimental result is from the accepted (theoretical) value, as a percentage of that accepted value.
Percent error = |Experimental − Theoretical| ÷ |Theoretical| × 100%
The three related quantities are:
- Absolute error = |Experimental − Theoretical| – in the same units as the measurement.
- Relative error = absolute error ÷ |Theoretical| – a unitless fraction.
- Percent error = relative error × 100.
Worked example
A pendulum experiment measures gravitational acceleration as 9.6 m/s². The accepted value is 9.81 m/s².
- Absolute error: |9.6 − 9.81| = 0.21 m/s².
- Relative error: 0.21 ÷ 9.81 ≈ 0.021407.
- Percent error: 0.021407 × 100 ≈ 2.14%.
The measurement was 2.14% too low – a respectable result for a school lab.
More examples
| Measured | True | Percent error |
|---|---|---|
| 98 °C (boiling water) | 100 °C | 2% |
| 1.05 g/cm³ (water density) | 1.00 g/cm³ | 5% |
| 340 m/s (speed of sound) | 343 m/s | ≈ 0.87% |
Why divide by the true value?
An error of 0.5 cm matters a lot when measuring a 2 cm bolt but hardly at all when measuring a 10 m room. Dividing by the accepted value puts every error on the same relative scale, so you can compare the quality of very different measurements fairly.
Reducing error in experiments
- Repeat measurements and average them to reduce random error.
- Calibrate instruments to remove systematic error – a consistent offset in one direction.
- Read scales at eye level to avoid parallax, and record the instrument’s precision.
- Keep the sign of the error in your notes: a consistently positive or negative error points to a systematic cause.
Frequently asked questions
Can percent error be negative?
The standard formula uses absolute values, so percent error is always zero or positive. Some lab courses keep the sign to show whether the measurement was too high (+) or too low (−); the calculator shows this signed error separately.
What is a good percent error?
It depends on the experiment. In school labs, under 5% is usually considered good and under 10% acceptable. Precision work in chemistry or physics may require well under 1%.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known true value. Percent difference compares two measurements when neither is known to be correct, dividing by their average instead of a true value.
Why can’t the true value be zero?
Percent error divides by the true value, and dividing by zero is undefined. If the accepted value is 0, report the absolute error instead.