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Percent Error Calculator

Find the percent error between a measured value and the true value.

How it is calculated

Percent error shows how far a measured result is from the accepted or theoretical value, relative to that true value: error % = |experimental − theoretical| ÷ |theoretical| × 100. The absolute value means the sign is dropped, so a reading that is too high and one that is too low by the same amount give the same percentage. The theoretical value is the denominator, so it must not be zero, otherwise there is no result. Both numbers should be in the same unit. The answer is a percentage, shown with two decimals. A smaller percentage means a more accurate measurement.

Worked example

A student measures the acceleration of gravity as 9.65 m/s² while the accepted value is 9.81 m/s². Difference: |9.65 − 9.81| = 0.16. Divide by the theoretical value: 0.16 ÷ 9.81 = 0.01631. Multiply by 100: 1.63%. The measurement is about one and a half percent off the accepted figure, and it would be the same 1.63% if the student had measured 9.97.

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Common mistakes

  • Swapping the two values. Dividing by the measured value instead of the theoretical one gives a different percentage.
  • Mixing units, such as a measurement in cm and a theoretical value in m.
  • Expecting a negative sign for an underestimate. The result is always positive, so it does not tell you the direction of the error.
  • Confusing percent error with percent difference between two measured values; here one value must be the accepted reference.

About this calculator

This calculator compares a measured (experimental) value against a known or accepted (theoretical) value and expresses the difference as a percentage of the theoretical value — the standard formula |measured − theoretical| / theoretical × 100 used to judge how accurate a measurement or estimate is.

It's a staple of school and university science labs, where a chemistry, physics or biology experiment's measured result (say, a boiling point or a measured density) is compared against the textbook or accepted value to judge how well the experiment went. It's also used more broadly in quality control and forecasting, wherever someone needs to quantify how far an estimate or reading strayed from the true or expected figure.

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