How far off were you?
When you measure or estimate something, you’re rarely exactly right. Percent error tells you how big your error is compared with the true value.
Percent error = |measured value − accepted value| ÷ accepted value × 100%
- The measured value (or experimental value) is what you found.
- The accepted value is the true or known value.
- The bars mean absolute value: ignore the sign, so the error is always positive.
Example: a science lab
You measure the boiling point of water as 98.5 °C. The accepted value is 100 °C.
- Error = |98.5 − 100| = 1.5
- 1.5 ÷ 100 = 0.015 → 1.5%
Example: an estimate
You estimate a room is 4.5 m long. It’s actually 4.2 m.
- Error = |4.5 − 4.2| = 0.3
- 0.3 ÷ 4.2 ≈ 0.071 → about 7.1%
Interpreting percent error
| Percent error | Accuracy |
|---|---|
| under 1% | excellent |
| 1–5% | good for most school labs |
| 5–10% | fair |
| over 10% | check your method |
What counts as "good" depends on the situation: 1% error is fine for a cake recipe but terrible for a medicine dose.
Percent error vs percent change
| Percent error | Percent change |
|---|---|
| compares measured vs true value | compares new vs original value |
| always positive (absolute value) | can be positive or negative |
| divide by the accepted value | divide by the original value |
Sources of error
- Instrument limits: a ruler marked only in cm.
- Human error: reading at an angle, reaction time with a stopwatch.
- Conditions: temperature, altitude (water boils below 100 °C at high altitude).
- Estimation: guessing instead of measuring.
Worked examples
Example 1: A student finds g = 9.5 m/s². Accepted: 9.8. Percent error?
0.3 ÷ 9.8 ≈ 3.1%.
Example 2: You guessed 120 jelly beans; there were 150. Percent error?
30 ÷ 150 = 20%.
Example 3: A scale reads 2.04 kg for a 2.00 kg mass. Percent error?
0.04 ÷ 2.00 = 2%.
Common mistakes
- Dividing by the measured value instead of the accepted value.
- Leaving a negative sign in the answer.
- Forgetting to multiply by 100 to make a percent.
Try it yourself
- Measured 52 cm, actual 50 cm. Percent error?
- Estimated 300 people, actual 250. Percent error?
- Lab result 0.95 g/mL, accepted 1.00 g/mL. Percent error?
- Why use the accepted value as the denominator?
Answers: 1) 4% 2) 20% 3) 5% 4) Because the error is measured relative to the true value.
Quick recap
- Percent error = |measured − accepted| ÷ accepted × 100%.
- It’s always positive and measures accuracy.
- Divide by the accepted value, not the measured one.