Measurement Uncertainty Calculator

This measurement uncertainty calculator turns an absolute uncertainty into a relative one and shows the range a measurement could lie in. Enter the measured value and its absolute uncertainty, the plus or minus figure, and the calculator returns the relative uncertainty as a percentage and the range from the lowest to the highest plausible value. Relative uncertainty tells you how precise a measurement is in proportion to its size, which is the fair way to compare instruments and readings. It is a staple of physics and chemistry lab work. The formula, a worked example and the assumptions are set out below.

Measured value

Absolute uncertainty (±)

Relative uncertainty

Value range

The formula

Relative uncertainty is the absolute uncertainty divided by the value, as a percentage: (uncertainty / value) times 100. The range is the value minus the uncertainty up to the value plus the uncertainty.

Worked example

A length of 10 with an uncertainty of 0.2 has a relative uncertainty of 0.2 / 10 = 2 percent, and a range of 9.8 to 10.2. Enter 10 and 0.2 to confirm.

Frequently asked questions

What is relative uncertainty?

The absolute uncertainty divided by the measured value, usually as a percentage. It shows precision relative to size.

What is the difference from absolute uncertainty?

Absolute uncertainty is the plus or minus in the same units. Relative uncertainty expresses that as a fraction of the value.

How do I report a measurement?

As value plus or minus uncertainty, for example 10.0 plus or minus 0.2, ideally with the relative uncertainty too.

Who this calculator is for

This calculator is for science students and anyone reporting the precision of a measurement.

What this calculator assumes

You enter a value and its absolute uncertainty.
Relative uncertainty is uncertainty over value.
Results are rounded for display.

Formula and sources

Related calculators

Scientific Calculator: general scientific maths.
Percentage Calculator: percentages and changes.
Ratio Calculator: simplify and scale ratios.

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