Relative Error Calculator
This relative error calculator works out how far a measured value strays from a true or accepted value, expressed as a percentage and a fraction rather than a raw number, so you can judge accuracy in proportion to the size of the quantity itself. Enter the measured value and the true (accepted) value, and the calculator instantly returns three figures: the relative error as a percentage, the same relative error written as a decimal fraction, and the absolute error, the plain difference between the two numbers before it is scaled. Relative error matters because absolute error alone is misleading: a one millimetre error is trivial on a ten metre wall but huge on a ten millimetre bolt, and relative error strips out that scale problem so measurements of very different sizes can be compared fairly. It is used constantly in science experiments, engineering tolerances, manufacturing quality control and financial forecasting, anywhere a measured or estimated figure is checked against a known or expected value. Update either field and the results recalculate immediately, so you can test several measurements against the same reference value in a row. Note that relative error is undefined whenever the true value is zero, since dividing by zero has no answer, so use a nearby non-zero reference in that case. Figures are rounded for display, so treat very small differences with care.
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
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