Percent Uncertainty Calculator
Convert an absolute uncertainty on a measurement to a percentage and back, and combine the uncertainties of two measurements that are multiplied or divided.
How big your measurement error is as a percentage, and how errors combine.
How the percent uncertainty calculator works
Relative (percent) uncertainty is the absolute uncertainty divided by the value: 25.0 ± 0.5 cm is ± 2%. When quantities are multiplied or divided, their percent uncertainties add (a simple rule; rigorous treatments add them in quadrature — the Detailed row shows both). When they are added or subtracted, the absolute uncertainties add instead.
Formula: % uncertainty = Δx ÷ x × 100 · product: %₁ + %₂ (simple) or √(%₁² + %₂²) (quadrature)
Worked examples
| Inputs | Percent uncertainty | Note |
|---|---|---|
| 25.0 ± 0.5 cm | 2% | 2% |
| 1.250 ± 0.005 kg | 0.4% | 0.4% |
| 25.0 ± 0.5 cm × 10.0 ± 0.1 cm | 2% | area: 3% (sum) or 2.24% (quadrature) |
FAQFrequently asked questions
What is the uncertainty of a ruler reading?
Usually half the smallest division — ± 0.5 mm for a millimeter rule — or the full division if the reading is hard to judge.
When do I add absolute and when percent uncertainties?
Absolute for sums and differences; percent for products, quotients and powers (a squared quantity doubles its percent uncertainty).
Simple sum or quadrature?
School courses usually add percentages; laboratory and engineering practice add them in quadrature (square root of the sum of squares) when the errors are independent.
How should I quote a result?
Round the uncertainty to one significant figure and the value to the same decimal place: 25.0 ± 0.5 cm, not 25.03 ± 0.5.
Where these figures come from
- IUPAC — Standard atomic weights (2021 conventional values) — the molar-mass table
- NIST — CODATA 2018 fundamental physical constants — Avogadro constant, gas constant, speed of light
- NIST Chemistry WebBook — thermochemical data
- National Institute of Standards and Technology — the US measurement and reference-data authority
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.