How do you calculate percentage uncertainty?

Divide the absolute uncertainty by the measured value and multiply by 100. For 2.50 ± 0.05 cm, the percentage uncertainty is 0.05 ÷ 2.50 × 100 = 2%.

How do you combine uncertainties?

Add the absolute uncertainties when adding or subtracting. Add the percentage uncertainties when multiplying or dividing. For a power, multiply the percentage uncertainty by the power.

How many significant figures should an uncertainty have?

Usually 1 significant figure, with the value given to the same number of decimal places, such as 2.37 ± 0.02 cm.

Percentage uncertainty calculator

Convert between absolute and percentage uncertainty, and combine uncertainties for sums, products, quotients and powers, with the working shown. It's free to use, with no sign-up.

Absolute and percentage uncertainty

Measured value

Absolute uncertainty (±)

or percentage uncertainty (%)

Percentage uncertainty = 0.05 ÷ 2.5 × 100 = 2%

Result: 2.50 ± 0.05

Combine two measurements

± uncertainty in a

Calculate

± uncertainty in b

Add the percentage uncertainties: 2% + 2% = 4%

10 × 5 = 50, and 4% of that is ± 2

Result: 50 ± 2 (4%)

Raise to a power

Measured value

± uncertainty

Power (e.g. 2, 3, 0.5, -1)

Percentage uncertainty in the value = 2.5%, so in the result = 2.5% × 2 = 5%

Result: 4² = 16, 16.0 ± 0.8

The rules for combining uncertainties

Adding or subtracting: add the absolute uncertainties.
Multiplying or dividing: add the percentage uncertainties.
Raising to a power: multiply the percentage uncertainty by the power (use its size if negative). So a squared quantity has double the percentage uncertainty.

For example, a length of 2.50 ± 0.05 cm has a percentage uncertainty of 0.05 ÷ 2.50 × 100 = 2%. Its square, an area estimate, has a percentage uncertainty of 2% × 2 = 4%.

How to write the answer

Give the uncertainty to 1 significant figure, and write the value to the same number of decimal places, such as 2.37 ± 0.02 cm. The percentage uncertainty is often given to 1 or 2 significant figures.

Common mistakes

Subtracting uncertainties when subtracting values: they always add.
Adding absolute uncertainties when multiplying or dividing, which needs percentages.
Forgetting to multiply the percentage uncertainty by the power.
Giving the uncertainty to too many significant figures.

Frequently asked questions

How do you calculate percentage uncertainty?: Divide the absolute uncertainty by the measured value and multiply by 100. For 2.50 ± 0.05 cm, the percentage uncertainty is 0.05 ÷ 2.50 × 100 = 2%.
How do you combine uncertainties?: Add the absolute uncertainties when adding or subtracting. Add the percentage uncertainties when multiplying or dividing. For a power, multiply the percentage uncertainty by the power.
How many significant figures should an uncertainty have?: Usually 1 significant figure, with the value given to the same number of decimal places, such as 2.37 ± 0.02 cm.

Practise it in a full required practical

LabWizard walks A-Level Physics students through simulated required practicals, from taking measurements with instruments like this one to graphing, analysis and exam questions.

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