Percent Error Calculator

Work out the percent error between a measured value and the true value, with absolute and relative error, a signed option and the working.

Reviewed by Dany, RightSums team · Updated

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maths · Daily life · UK & US

Enter what you measured and the true, accepted or theoretical value, and the calculator gives the percent error: the difference between them, ignoring the sign, divided by the size of the true value and multiplied by 100. It also shows the absolute error and the relative error. Tick the signed option to see if you were over or under: a positive signed error means the measurement was too high and a negative one means it was too low. Choose how many decimal places to show. The arithmetic is exact until the final rounding. Percent error cannot be worked out when the true value is 0, because that would mean dividing by zero. It is common in physics and chemistry lab reports.

Accepted inputs

  • Measured (experimental) value
  • True (accepted or theoretical) value
  • Decimal places
  • Signed error option

Outputs

  • Percent error
  • Signed percent error
  • Absolute error
  • Relative error
  • Step-by-step working

How to use the Percent Error Calculator

  1. Enter your measured value and the true or accepted value.
  2. The calculator subtracts the true value from the measured value and ignores the sign to get the absolute error.
  3. It divides the absolute error by the size of the true value and multiplies by 100 to give the percent error.
  4. With the signed option on, it keeps the sign so you can see if your measurement was too high or too low.

Frequently asked questions

What is the formula for percent error?

Percent error = |measured − true| ÷ |true| × 100. The vertical bars mean you ignore any minus sign. If you measured 52 and the true value is 50, the error is 2, and 2 ÷ 50 × 100 = 4%.

How do you calculate percent error in a physics experiment?

Subtract the accepted value from your result, ignore the sign, divide by the accepted value and multiply by 100. If you measured g as 9.6 m/s² and the accepted value is 9.81 m/s², the error is 0.21, and 0.21 ÷ 9.81 × 100 = 2.14%.

Can percent error be negative?

Standard percent error is never negative, because it uses the size of the difference. Some courses use a signed version that keeps the sign: positive when the measurement is too high, negative when it is too low. The 9.6 against 9.81 example gives a signed error of −2.14%.

What is the difference between absolute, relative and percent error?

Absolute error is the size of the difference, in the same units as the measurement. Relative error is that difference divided by the true value. Percent error is the relative error times 100. Measuring 340 m/s against 343 m/s gives an absolute error of 3 m/s and a percent error of 0.87%.

What if the true value is zero?

Percent error cannot be calculated when the true value is 0, because the formula divides by it. In that case report the absolute error instead, the plain difference between your measurement and the expected value, with its units. The calculator shows a message rather than a result.

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