Percent error calculator (and percent difference)
Enter your values. The answer and the full worked solution update as you type.
Result
Compare a measured value with the accepted value: the calculator gives the absolute error, the relative error and the percent error, and says whether the measurement is too high or too low. Two other modes give the percent difference between two measurements where neither is the true value, and the percent change from an old value to a new one.
Step-by-step solution
Absolute error
Relative and percent error
Key formulas
- Percent error
- |measured − accepted| / |accepted| × 100%
- Percent difference
- |x1 − x2| / ((x1 + x2)/2) × 100%
- Percent change
- (new − old) / |old| × 100%
How to calculate percent error
- Subtract the accepted (true or theoretical) value from the measured value. This is the error; its size without the sign is the absolute error.
- Divide the absolute error by the absolute value of the accepted value. This is the relative error.
- Multiply by 100% to get the percent error: |measured − accepted|/|accepted| × 100%.
- Keep the sign if you want to show the direction: a negative signed error means the measured value is too low.
- If neither value is the accepted one, use the percent difference instead and divide by the mean of the two values.
Questions and answers
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known accepted value and divides by that value. Percent difference compares two measurements of equal standing and divides by their mean, so swapping the two values gives the same result.
Can percent error be negative?
The usual percent error uses the absolute value, so it is always positive. Some courses keep the sign to show whether the result is too high or too low; the calculator gives both.
What is a good percent error?
It depends on the experiment. In a school lab a few percent is often acceptable; in precise work much less is expected. An error above 100% usually means a mistake such as a wrong unit rather than an inaccurate measurement.
How is percent change different?
Percent change measures how much a quantity grew or shrank compared with its old value: (new − old)/|old| × 100%. A price going from 80 to 92 has risen by 15%.
Practise it yourself
Practise Descriptive statistics
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.