Uncertainty & measurement
Percentage Error & Difference Calculator
Choose error when you have an accepted reference, or difference when neither measurement is the reference.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
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Result & working
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Step-by-step working
The formula
Error = |experimental − accepted| / |accepted| × 100%
Difference = |a − b| / [(|a| + |b|)/2] × 100%
Signed change = (new − initial) / |initial| × 100%
| Symbol | Meaning |
|---|---|
| Experimental | The measured or experimental result. |
| Accepted | A non-zero reference value used for percentage error. |
| a, b | Two values with equal standing, used for percentage difference. |
When to use this calculator
Percentage error measures how far an experimental result is from an accepted value; reversing the inputs usually changes the answer. Percentage difference is symmetric and measures separation relative to the average magnitude. Signed percentage change compares a new value with a non-zero initial value using its magnitude as the denominator; the sign indicates an increase or decrease.
With two measurements 10 and 12, percentage difference is 2/11 × 100 ≈ 18.18%. If 12 is the accepted reference, percentage error is 2/12 × 100 ≈ 16.67%. The formulas answer different questions.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- Percentage error = |experimental − accepted| / |accepted| × 100
- = |9.7 − (9.81)| / |9.81| × 100 = 1.121305%
1.121305%
Common mistakes
- Do not call percentage difference a measurement uncertainty.
- A zero accepted value makes percentage error undefined.
- Both values zero make percentage difference undefined; opposite signs can give 200% under this convention.