How far a measured value is from the true value.
A percentage error calculator shows how far a measurement is from the true or accepted value, as a percentage of that true value. It is used in science labs, engineering and quality checks. Enter your experimental result and the accepted value, and you get the percent error, the absolute error, the relative error and whether your result was over or under, with the steps written out ready for a lab report.
How to Use the Percent Error Calculator
- Measured (experimental) value: the result you got.
- True (accepted) value: the textbook, reference or known value.
- Read the percent error, plus the absolute error, the relative error and the direction (over or under the true value).
The Percent Error Formula
Percent error = |Measured − True| ÷ |True| × 100
- Absolute error = Measured − True. It keeps its sign, so it tells you whether you were over or under.
- Relative error = Absolute error ÷ True value, as a decimal.
- Percent error is the size of the relative error as a percentage.
How to Calculate Percent Error in 4 Steps
- Subtract the true value from your measured value.
- Ignore the minus sign, if there is one.
- Divide by the true value.
- Multiply by 100 to get a percentage.
Percent Error Examples
Measuring gravity with a pendulum. Your result is 9.6 m/s², and the accepted value is 9.81 m/s².
Error = 9.6 − 9.81 = −0.21. Percent error = 0.21 ÷ 9.81 × 100 = 2.14%, under the true value. The relative error is about −0.0214.
Boiling point of water. You measure 98.2 °C against the standard 100 °C at sea level.
Error = 1.8, so the percent error is 1.8 ÷ 100 × 100 = 1.8%, under.
Density of aluminum. You measure 2.65 g/cm³ against an accepted 2.70 g/cm³.
Error = 0.05, so the percent error is 0.05 ÷ 2.70 × 100 = 1.85%.
What Counts as a Good Percent Error?
It depends on the experiment and the equipment. As a rough guide for school labs:
| Percent error | What it usually means |
|---|---|
| Under 1% | Very accurate, often with good equipment |
| 1% to 5% | Typical for a careful school experiment |
| 5% to 10% | Worth explaining in your evaluation |
| Over 10% | Check for a method problem or a calculation slip |
Your teacher or course may set its own targets, so check those first.
Writing About Percent Error in a Lab Report
- State the result and the accepted value, with units.
- Give the percent error to a sensible number of decimal places, usually two.
- Say whether you were over or under. A consistent direction often points to a systematic error, such as a scale that is not zeroed.
- Suggest causes, such as reaction time, heat loss, air resistance or reading the scale at an angle.
- Suggest an improvement, such as repeating readings and taking an average.
Percent Error vs Percentage Difference
Use percent error when one value is known to be correct. Use the percentage difference calculator when you are comparing two measurements and neither one is the accepted value.
Percent Error FAQs
Can percent error be negative?
Percent error is usually reported as a positive number, because it measures the size of the error. The sign of the absolute error tells you the direction, which the calculator shows separately.
Why do you divide by the true value?
The error is measured relative to the correct answer, so the true value is the fair point of comparison.
What if the true value is zero?
Percent error cannot be calculated, because you cannot divide by zero. Report the absolute error instead.
Is percent error the same as percentage error?
Yes. Both names describe the same formula.
For more help with lab calculations, see the velocity calculator for motion experiments, or our list of basic math formulas.
How we checked this page: every example was worked by hand and matches the calculator’s percent, absolute and relative error.