Quick answer: Measuring g as 9.6 m/s² when the accepted value is 9.81 gives |9.6 − 9.81| ÷ 9.81 × 100 = 0.21 ÷ 9.81 × 100 ≈ 2.1407% error.
How it's calculated
Percent error = |measured − true| ÷ |true| × 100. The absolute value makes it positive, so it tells you how big the error is, not its direction.
The signed error, (measured − true) ÷ true × 100, keeps the sign: negative means the measurement was too low, positive too high. Relative error is the same ratio without the × 100.
Percent error compares against a fixed true value. To compare an old value with a new one, use percentage change instead; the formula looks similar but the meaning differs.
Worked examples
- Measured 9.6, true 9.81: 0.21 ÷ 9.81 × 100 = 2.1407%
- Measured 52, true 50: 2 ÷ 50 × 100 = 4%
- Measured 0.98 L, true 1 L: 0.02 ÷ 1 × 100 = 2%
Frequently asked questions
Can percent error be negative?
The usual percent error uses an absolute value, so it is never negative. The signed error shown beside it can be negative, meaning the measurement was below the true value.
What is a good percent error?
In school lab work a few percent is usually fine. Precise measurements aim for far less, so it really comes down to the instrument and the task.
Why can't the true value be zero?
The formula divides by the true value, and dividing by zero is undefined. Use the absolute error instead.
What is the percent error of 9.6 against 9.81?
About 2.14%. Your measurement came in low, so the signed error is −2.14%.
What's the difference between percent error and percent difference?
Percent error compares your result with a known true value. Percent difference compares two measurements when neither one is the true value, and divides by their average.
How do I reduce percent error in an experiment?
Repeat the measurement and average the results, use a more precise instrument, and watch for errors that always push the same way, like a scale that isn't zeroed.