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Percent Error Calculator
Enter a measured value and the accepted value to get the percent error, with the working. A second mode finds the percent difference between two measurements when neither is the reference.
The percent error formula
Percent error measures how far a measurement lies from a value accepted as correct, relative to that accepted value: percent error = |measured − accepted| ÷ |accepted| × 100. The bars mean absolute value, so the answer is never negative. Some textbooks omit the absolute value and keep the sign, which tells you whether you overshot or undershot. This page shows both, labelling the signed version separately.
For a measured 9.5 against an accepted 9.81, the absolute error is 0.31, and 0.31 ÷ 9.81 × 100 is about 3.16%.
Percent difference is a different quantity
Percent error needs a reference value you trust. When you are comparing two measurements of the same thing and neither is the standard, use percent difference instead: |a − b| ÷ ((a + b) ÷ 2) × 100. Dividing by the average makes the result symmetric, so swapping the two values gives the same answer.
Mixing the two up is a frequent error in lab reports. Ask whether one number is a reference. If it is, use percent error. If both are just results, use percent difference. The two formulas give different figures for the same pair of numbers, because they divide by different bases.
Interpreting the size of the error
A small percent error suggests the measurement is close to the accepted value, but what counts as small depends on the instrument and the field. A kitchen scale and an analytical balance have very different expected precision. Compare your figure with the stated tolerance of your equipment, not with a universal threshold.
Percent error also hides the difference between accuracy (closeness to the true value) and precision (repeatability). Repeated readings can agree closely with each other and still sit far from the true value because of a systematic error such as a miscalibrated instrument. A single percent error figure cannot reveal this, which is why repeated trials and an uncertainty estimate are good practice.
Pitfalls and edge cases
- Accepted value of zero. Percent error is undefined because it divides by the accepted value. Quote the absolute error instead.
- Units must match. Convert both numbers to the same unit first, such as both in metres or both in kelvin.
- Temperature scales. Percent error on Celsius or Fahrenheit readings depends on the arbitrary zero point. Convert to kelvin for a meaningful ratio.
- Rounding. Do the calculation with unrounded numbers and round only the final answer.
Percent error is a ratio and has no unit of its own. It can exceed 100% when the measurement is more than twice the accepted value.
Worked example
A student measures gravitational acceleration as 9.5 m/s² in a lab experiment, and compares it with the accepted value of 9.81 m/s².
Inputs
| What do you want to find? | Percent error (measured vs accepted value) |
|---|---|
| Measured (experimental) value | 9.5 |
| Accepted (true) value | 9.81 |
Result
The measurement is below the accepted value.
| Absolute error | 0.31 |
|---|---|
| Signed (relative) error | -3.16% |
| Working | |9.5 − 9.81| ÷ |9.81| × 100 |
Accuracy note: Results use standard double-precision arithmetic, so very large or very small values may be rounded. Check important results by another method.
Frequently asked questions
How do I calculate percent error?
Subtract the accepted value from the measured value, take the absolute value, divide by the accepted value, and multiply by 100. A measurement of 9.5 against 9.81 gives about 3.16%.
Can percent error be negative?
The usual definition uses an absolute value, so it is never negative. If you keep the sign, a negative result means the measurement was below the accepted value.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a trusted reference, whereas percent difference compares two values on equal footing by dividing by their average.
Is a lower percent error always better?
Generally yes for accuracy, but a very low figure from one reading may be luck. Repeated trials and an uncertainty estimate give a fuller picture.
Why can I not use zero as the accepted value?
The formula divides by the accepted value, and division by zero is undefined. In that situation report the absolute error in the measurement units.
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References and sources
- NIST Guide to the SI and NIST Technical Note 1297 on evaluating and expressing measurement uncertainty. Link