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Percent Error Calculator

Compare a measured value with the accepted value to get the percent error, signed error, absolute error and relative error, or find the percent difference between two values.

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The experimental or observed result.
The accepted, true or expected value. It cannot be 0.

Read the guide How to Calculate Percent Error in a Lab Report

How to use the calculator

Choose Percent error when you have a measurement and a known reference value, for example a lab result and the value from a textbook. Enter the measured (experimental) value and the theoretical (accepted) value, then press Calculate.

Choose Percent difference when you compare two values and neither one is the reference, such as two measurements of the same object taken with different instruments.

The result card shows the main percentage together with the related error figures, and the details panel lists every step with your numbers.

Formulas

  • Signed error: E − T
  • Absolute error: |E − T|
  • Relative error: |E − T| / |T|
  • Percent error: |E − T| / |T| × 100
  • Percent difference: |A − B| / ((A + B) / 2) × 100

Here E is the measured value, T the theoretical value, and A and B the two values being compared. The signed error keeps the direction: it is negative when the measurement is too low and positive when it is too high.

Worked examples

Gravity experiment. A pendulum experiment gives 9.7 m/s², while the accepted value is 9.81 m/s². The signed error is 9.7 − 9.81 = −0.11, the absolute error is 0.11, the relative error is 0.11 / 9.81 ≈ 0.0112130479, and the percent error is about 1.121304791%. The measurement is a little low.

Two measurements. One scale reads 10 kg and another reads 15 kg. The difference is 5 and the average is 12.5, so the percent difference is 5 / 12.5 × 100 = 40%.

Good to know

  • Percent error is undefined when the theoretical value is 0, because the formula divides by it. In that case report the absolute error instead; the calculator shows it in the message.
  • The denominator uses the size of the theoretical value, so a negative accepted value such as −40 °C still gives a positive percent error.
  • Percent difference treats both values equally, so swapping A and B gives the same answer. It is meant for two values with the same sign.
  • A small percent error means the measurement is accurate. It does not tell you how precise repeated measurements are; for that, look at their spread.
  • Results are shown with up to 10 significant digits.

Frequently asked questions

Can percent error be negative?

The usual percent error uses the absolute value, so it is never negative. Some courses use a signed version without the absolute value to show whether a measurement is too high or too low. The calculator shows both: the percent error and the signed percent error.

What is the difference between percent error and percent difference?

Percent error compares a measurement with a known correct value and divides by that correct value. Percent difference compares two values of equal standing and divides by their average, because neither one is the reference.

What is a good percent error?

It depends on the field and the equipment. In a school lab, a few percent is often acceptable, while precise engineering or analytical chemistry can require well under 1%. Check the tolerance your teacher, method or specification sets.

Why can I not use 0 as the theoretical value?

Percent error divides the error by the theoretical value, and dividing by zero is undefined. When the accepted value is 0, describe the result with the absolute error, which is simply the distance between the measurement and 0.