Uncertainty & measurement
Percentage Uncertainty Calculator
How large is the uncertainty compared with the measurement? Enter a value and its absolute uncertainty in the same units.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
Calculated locally. No account or uploads.
Result & working
ExampleThe calculator is loading. You can read the worked example below.
Step-by-step working
The formula
p = (Δx / |x|) × 100%
| Symbol | Meaning |
|---|---|
| x | Measured value; it may be negative, but not zero. |
| Δx | Non-negative absolute uncertainty, in the same unit as x. |
| p | Percentage uncertainty. |
When to use this calculator
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.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- 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
0.6637168%
Common mistakes
- 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.