Percent Error Calculator
Percent error = |measured − true| ÷ |true| × 100: how far a measurement is from the true value, whether it was high or low, and the percent difference when neither is true.
Result
Percent error: 0.1019%
Percent error measures against a true value; percent difference, against the average of the two.
- Relative error, signed
- -0.1019%
- Absolute error
- 0.01
- The measurement was
- Lower than the true value
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How to use the Percent Error Calculator
- Choose whether you are comparing a measurement with a true value, or two measurements.
- Enter the measured value and the true value, or the two measurements.
- Read the percent error and whether the measurement was high or low, or the percent difference.
The formulas
percent error = |measured − true| ÷ |true| × 100percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100The absolute value in the denominator keeps the percentage positive when the true value is negative: −5 against −10 is a 50% error.
Which to use
Use percent error when one value is accepted as correct, such as a textbook constant or a calibrated standard. Use percent difference when comparing two readings, two instruments or two methods, none of which is the reference.
With your numbers
- |9.8 − 9.81| = 0.01
- 0.01 ÷ |9.81| × 100 = 0.101937%
Quick reference
Percent error measures against a true value; percent difference, against the average of the two.
| Example | Result |
|---|---|
| 9.8 against 9.81 | Percent error: 0.1019% |
| 105 against 100 | Percent error: 5% |
| 95 against 100 | Percent error: 5% |
| 105 and 100, difference | Percent difference: 4.878% |
| −5 against −10 | Percent error: 50% |
| 5 against 0 | Percent error: |
Common questions about the Percent Error Calculator
- What is the difference between percent error and percent difference?
- Percent error compares a measurement with a value known to be right, and divides by that true value. Percent difference compares two values when neither is known to be right, and divides by their average. 105 against a true 100 is a 5% error; 105 and 100 as two measurements differ by 4.88%.
- Is percent error always positive?
- By the usual definition, yes: it uses the size of the gap. The page also gives the signed relative error, so you can see whether the measurement was high or low: 105 against 100 is +5%, 95 is −5%.
- Why is percent error undefined when the true value is zero?
- Because it divides by the true value, and dividing by zero has no meaning. Any gap at all from zero would be an infinitely large percentage. Report the absolute error instead.
- How is this different from percentage change?
- Percentage change measures how much a value moved from a starting value to a new one, as the percentage change calculator does. Percent error measures how far a result is from the right answer. The arithmetic is similar; the meaning is not.