How to calculate percent error
- Enter your Measured value, the result you got from the experiment or estimate.
- Enter the True value, the accepted or theoretical figure you're comparing against.
- Read the percent error, whether your measurement is high or low, the absolute error and the signed percent error.
Worked example
A student times a pendulum and works out the acceleration due to gravity as 9.6 m/s². The accepted value is 9.81 m/s².
- Absolute error: |9.6 − 9.81| = 0.21
- Divide by the true value: 0.21 ÷ 9.81 = 0.021407 (this is the relative error)
- Multiply by 100: 2.1407%
The measurement is low, so the signed percent error is −2.1407%. The units cancel out in step 2, so percent error has no units, whatever you measured.
Mistakes that change the answer
- Dividing by the measured value. The bottom of the fraction is always the true value. Dividing 0.21 by 9.6 instead gives 2.1875%, which is wrong.
- Forgetting to multiply by 100. 0.0214 is the relative error. As a percentage it’s 2.14%.
- Rounding too early. Keep all the digits until the end, then round the final answer to match the precision of your data.
- A true value of 0. Percent error divides by the true value, so it can’t be worked out when that’s 0. Report the absolute error instead.
A small percent error means your result is accurate, close to the true value. It says nothing about precision, which is how close repeated measurements are to each other. For that, take several readings and look at their standard deviation.