Compare a measured value with the accepted value to get the percent error, or compare two measurements with the percent difference.
How percent error is calculated
Percent error = |experimental − theoretical| ÷ |theoretical| × 100
Most chemistry and physics classes use the absolute value, so percent error is never negative. The signed version, (experimental − theoretical) ÷ |theoretical| × 100, also shows the direction: negative means your measurement was too low.
Example: you measure gravity as 9.6 m/s², and the accepted value is 9.81 m/s². The error is |9.6 − 9.81| = 0.21, and 0.21 ÷ 9.81 × 100 = 2.14%. The signed error is −2.14%, because the measurement was low.
Percent difference
When neither value is the "right" one, such as two students' measurements, compare the difference with their average instead:
Percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100
Example: 10 and 12 differ by 2, and their average is 11, so the percent difference is 2 ÷ 11 × 100 = 18.18%. Percent difference gives the same answer whichever value comes first. Percent change doesn't: 10 to 12 is +20%, but 12 to 10 is −16.67%. For that, use the percentage calculator.
When percent error misleads
- It's undefined when the true value is 0, and huge when the true value is close to 0. Report the absolute error instead.
- On interval scales like °C or °F, the zero point is arbitrary, so percent error depends on the unit. Converting to kelvin gives a different, more meaningful result.
- A small percent error doesn't prove a method is precise. Repeated measurements and their standard deviation show that.
Sources
How we checked this
Before every update, this calculator is run in a real browser with these known answers, and it must match all of them:
- −5 and 5: average size label, not 'average' ✓
- Measured 9.6, true 9.81: 2.1406728% ✓
- Signed error is −2.1406728% (too low) ✓
- Negative true value: −4.5 vs −5 is +10% ✓
- Percent difference of 10 and 12 = 18.181818% ✓
- A true value of 0 is rejected ✓
Last checked October 26, 2026. Spotted something wrong? The math is done in your browser with the formula shown on this page, so you can check any result by hand.
Questions people ask
How do you calculate percent error?
Subtract the true value from your measurement, ignore the sign, divide by the true value and multiply by 100.
Can percent error be negative?
With the usual absolute-value formula, no. If your class uses the signed version, a negative result means the measurement was below the true value.
What is a good percent error?
It depends on the experiment. In many school labs, under 5% is considered good, but precise work may need far less. Check what your instructor expects.
What's the difference between percent error and percent difference?
Percent error compares a measurement with a known true value. Percent difference compares two values when neither is known to be correct, using their average as the base.