Relative Error Calculator

This relative error calculator works out the relative error of a measurement, the absolute error expressed as a fraction or percentage of the true value. Enter the measured and true values and the calculator returns the relative error as a percentage and as a decimal fraction, with the absolute error alongside. Relative error is the fairer way to compare accuracy across different scales, because a one millimetre error matters far more on a pencil than on a road. It is widely used in science, engineering and finance. The formula, a worked example and the assumptions are set out below.

Measured value

True (accepted) value

As a fraction

Absolute error

The formula

Relative error is the absolute error divided by the absolute value of the true value: |measured − true| / |true|. Multiply by 100 to express it as a percentage. It is dimensionless.

Worked example

Measuring 9.8 against a true value of 10 gives a relative error of |9.8 − 10| / 10 = 0.02, or 2 percent. Enter 9.8 and 10 to confirm.

Frequently asked questions

What is relative error?

The absolute error divided by the true value, usually written as a percentage. It shows the error in proportion to the quantity.

Why use relative error?

It lets you compare the accuracy of measurements on different scales, which raw absolute error cannot do.

What if the true value is zero?

Relative error is undefined when the true value is zero, since you cannot divide by zero.

Who this calculator is for

This calculator is for students and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid numbers.
The standard formula is applied.
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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