Percent Error Formula & Calculator
How far a measured value is from the accepted value, as a percentage of the accepted value.
Error = |9.6 − 9.81| = 0.210.21 ÷ |9.81| × 100 = 2.1407%
How to calculate percent error
- Subtract the accepted (true) value from your measured value.
- Take the absolute value, so the error is positive.
- Divide by the accepted value and multiply by 100.
Examples
| Experiment | Measured | Accepted | Working | Percent error |
|---|---|---|---|---|
| Gravity (m/s²) | 9.6 | 9.81 | 0.21 ÷ 9.81 × 100 | 2.141% |
| Volume in a beaker (mL) | 48.5 | 50 | 1.5 ÷ 50 × 100 | 3% |
Percent error vs. percent change
The arithmetic is the same shape as percent change: a difference divided by a reference value. The difference is in meaning. With percent error the reference is the correct value and the sign is usually dropped; with percent change the reference is the earlier value and the sign tells you the direction.
Sources of error to mention in a lab report
- Random error: scatter from reading instruments, timing by hand or small changes in conditions. Reduce it by repeating the measurement and averaging.
- Systematic error: a consistent bias, such as a scale that isn’t zeroed or an uncalibrated thermometer. Repeating doesn’t fix it; recalibrating does.
- Rounding: keep full precision until the final step, then round the percent error.
Frequently asked questions
What is the percent error formula?
Percent error = |measured value − accepted value| ÷ |accepted value| × 100.
Can percent error be negative?
With the absolute-value formula, no. Some science courses drop the absolute value to show whether the measurement was too high (positive) or too low (negative); check which convention your course uses.
What is a good percent error?
It depends on the experiment. In many school labs, under about 5% is considered good, but precise instruments and professional work expect far smaller errors.
How is percent error different from percent difference?
Percent error compares a measurement to a known correct value and divides by that correct value. Percent difference compares two values when neither is known to be correct and divides by their average.