Uncertainty & measurement
Percentage uncertainty
Express an absolute uncertainty as a percentage.
Your measurements
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.
Calculated locally. No account or uploads.
Result & working
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Interpretation & assumptions
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Measured value; it may be negative, but not zero. | |
| Non-negative absolute uncertainty, in the same unit as x. | |
| Percentage uncertainty. |
Worked example
- Measured value x
- 4.52
- Absolute uncertainty Δx
- 0.03
- Result unit (optional)
- V
- Uncertainty significant figures
- 1 significant figure
0.6637168%
Follow the example steps
- Percentage uncertainty = Δx / |x| × 100
- = 0.03 / |4.52| × 100 = 0.6637168%
- Round the uncertainty first; match the decimal place of the value: (4.52 ± 0.03) V
Common mistakes
Use matching units for the value and its absolute uncertainty.
Incorrect approach
x = 10 cm, Δx = 1 mm: 100 × 1/10 = 10%
Correct approach
Δx = 0.1 cm: 100 × 0.1/10 = 1%
More checks before you submit
- Do not enter 3 when you mean an absolute uncertainty of 0.03.
- Convert value and absolute uncertainty to the same unit first.
- Keep extra digits while calculating; round the final measurement only.
Method notes
Use percentage uncertainty to compare relative precision across measurements of different sizes. A voltage uncertainty of 0.03 V matters much more beside 0.2 V than beside 20 V.
The sign of a reading does not make its uncertainty negative, so the denominator is |x|. A reading of zero can have an absolute uncertainty, but its percentage uncertainty is undefined.