Uncertainty & measurement
Percentage error & difference
Compare measured and reference values.
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Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
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Result & working
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Interpretation & assumptions
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Experimental | The measured or experimental result. |
| Accepted | A non-zero reference value used for percentage error. |
| Two values with equal standing, used for percentage difference. |
Worked example
- Comparison
- Percentage error
- Experimental / new value / value a
- 9.7
- Accepted / initial value / value b
- 9.81
1.121305%
Follow the example steps
- Percentage error = |experimental − accepted| / |accepted| × 100
- = |9.7 − (9.81)| / |9.81| × 100 = 1.121305%
Common mistakes
Percentage error uses the accepted value as denominator.
Incorrect approach
a = 12, b = 10: 100 × 2/12 ≈ 16.7%
Correct approach
100 × |12 − 10|/|10| = 20%
More checks before you submit
- 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.
Method notes
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.