Percent Error Calculator
Percent error of a measured value against the true value, |measured − true| ÷ |true| × 100, signed if you want, or the percent difference of two values. How it works
Use the Percent Error Calculator
About the Percent Error Calculator
Percent error is |measured − true| ÷ |true| × 100. A measured 9.8 against a true value of 10 is a 2% error. This percent error calculator shows that working with your own numbers, and it can give the signed result (-2% here) when you need to know whether the measurement was high or low.
Percent error examples: absolute and signed
| Measured | True | Percent error | Signed percent error |
|---|---|---|---|
| 9.8 | 10 | 2% | -2% |
| 102 | 100 | 2% | +2% |
| 9.6 | 9.81 | 2.14067% | -2.14067% |
| 3.14 | 3.14159 | 0.0506113% | -0.0506113% |
| 24.5 | 25 | 2% | -2% |
| 105 | 100 | 5% | +5% |
| 0.52 | 0.5 | 4% | +4% |
| 48 | 50 | 4% | -4% |
| 330 | 343 | 3.79009% | -3.79009% |
| 2.5 | 2.7 | 7.40741% | -7.40741% |
| 150 | 100 | 50% | +50% |
| -9 | -10 | 10% | +10% |
The signed result is positive when the measured value is above the true value. The divisor is the absolute value of the true value, so -9 against -10 is +10%.
How to use this tool
- Type the measured (experimental) value and the true (accepted or theoretical) value.
- Choose Absolute for the usual result, which is never negative, or Signed to keep the direction. For two measurements with no true value, set Calculation type to Percent difference.
- Read the percent and the line of working under it.
Frequently asked questions
- How do you calculate percent error?
- Subtract the true value from the measured value, take the absolute value, divide by the absolute value of the true value and multiply by 100. For a measured 24.5 and a true 25: |24.5 − 25| ÷ |25| × 100 = 2%.
- Can percent error be negative?
- Not in the absolute form, which never goes below 0. The signed form can: it is negative when the measured value is below the true value. A measured 48 against a true 50 is 4% absolute and -4% signed, and a measured 105 against 100 is +5% signed.
- What is the difference between percent error and percent difference?
- Percent error compares a measurement with a known true value and divides by that true value. Percent difference compares two measurements when neither is the reference, and divides by the mean of their sizes: |a − b| ÷ ((|a| + |b|) ÷ 2) × 100, so −5 and 5 differ by 200%. Set Calculation type to Percent difference: 8 and 12 give 40%, and 9.8 and 10 give 2.0202%. For percent change from an old value to a new one, use the Percentage Calculator.
- What happens when the true value is 0?
- Percent error is undefined, because the formula divides by the true value. The tool says so and gives the absolute error in its place: a measured 5 against a true 0 has an absolute error of 5.
- What is a good percent error?
- There is no general cutoff, and the tool does not grade the result. What is acceptable depends on the instrument and the experiment, so use the limit your course or lab protocol sets.
- Does it matter which number goes in as the true value?
- Yes. The error is divided by the true value, so swapping the two changes the answer: 9.8 measured against 10 is 2%, and 10 measured against 9.8 is 2.04082%.
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