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Percentage Error Calculator

Enter your measured and true values to compute the percentage error.

Result

2.14%
0.2100
0.0214

How it is calculated

The tool compares your measurement with the accepted value and returns three numbers. absolute error = |measured − true|, relative error = absolute error / |true| (a fraction) and percentage error = relative error × 100. The absolute value means a reading that is too high and one that is too low by the same amount give the same result, so the sign of the deviation is lost. Percentage error and relative error are scaled by the true value, not by your measurement. The two inputs must be in the same unit, and the true value cannot be 0, because the division would be undefined; absolute and relative error are shown to 4 decimals and the percentage to 2.

Worked example

In a lab you measure g as 9.6 m/s², while the accepted value is 9.81. Absolute error = |9.6 − 9.81| = 0.2100. Relative error = 0.21 / 9.81 = 0.0214. Percentage error = 0.0214 × 100 = 2.14%. If you had measured 10.2 instead, the absolute error would be 0.39 and the percentage error 3.98%, even though the reading is above the true value rather than below it.

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Common mistakes

  • Swapping the two fields. Dividing by your measurement instead of the accepted value gives a different percentage, so enter the true (reference) value in the true-value field.
  • Using this for a comparison of two experimental values. Percentage error needs a reference value you trust; for two measurements with no known truth, use a percentage difference instead.
  • Reading the result as a signed number. The result is an absolute value, so it does not tell you whether the measurement was too high or too low.
  • Mixing units, for example a measured value in centimetres against a true value in metres. Both must be in the same unit before you enter them.
  • Entering a true value of 0. The percentage error is undefined then, and the tool gives no result.

About this calculator

Percentage error quantifies how far a measured or experimental value strays from the true, accepted value, expressed as a share of that true value rather than as a raw difference: %Error = |measured − true| / |true| × 100, using the absolute value so the result reads as a magnitude of deviation regardless of whether the measurement came in high or low.

This is a staple calculation in physics and chemistry lab reports, engineering measurement validation, and any experimental setting where a result needs to be judged against a known reference — a low percentage error indicates a precise and accurate measurement technique, while a high one flags instrument calibration issues, procedural mistakes, or the limits of the measuring equipment.

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Comments (1)

  • Editorial team

    Percentage error depends heavily on how big the true value is. A reading of 11 against a true value of 10 is 10.00 percent off, while 0.5 against 0.1 is 400.00 percent, even though the absolute gap is only 0.4000. So when the reference value is small, quote the absolute error as well. A result near 99.00 percent, like 1 against 100, usually points to a slipped decimal point. Which kind of measurements do you check with it?

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