Percent error calculator

Percent error between a measured and a true value, plus absolute error and percent difference.

Measured (experimental) value

True (accepted) value

About the percent error calculator

Percent error between a measured and a true value, plus absolute error and percent difference.

Part of SmartCalcy’s math tools. It runs in your browser with no account, uses your own currency and units (change them at the top of the page), and gives estimates for information only, so check official guidance before you rely on a result.

How to use the percent error calculator

What it calculates and when to use it

Compares a measured or estimated value with the true or accepted value and states the gap as a percentage. It is used in science labs, engineering checks and forecasting.

How to use it, step by step

Enter the value you measured.
Enter the true or accepted value.
Read the percent error, absolute error and signed error.

What each input means

Measured value – The experimental, observed or estimated result.
True value – The theoretical or accepted value. It cannot be zero.

How to read the results

Percent error – The size of the error as a percentage of the true value.
Signed error – Positive if you measured too high, negative if too low.
Percent difference – Compares two values with neither one treated as correct.

The formula

Percent error = |measured − true| ÷ |true| × 100. Percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100.

A worked example

A student measures gravitational acceleration as 9.6 m/s² when the accepted value is 9.81. The absolute error is 0.21, so the percent error is 0.21 ÷ 9.81 × 100 = 2.141%, and the signed error is −2.141% because the measurement is low.

Assumptions and limits

The true value is known and non-zero.
Units must match.

Common mistakes

Dividing by the measured value instead of the true value.
Using percent error when there is no accepted value.

Frequently asked questions

Can percent error be negative?

The standard definition uses the absolute value, so it is positive. The signed error shows direction.

What if the true value is zero?

Percent error is undefined. Use absolute error instead.

Percent error

2.141%

-0.21 difference from the true value

Details

Absolute error: 0.21
Signed error: -2.141%measured value is below the true value
Percent difference: 2.164%relative to the average of the two values

Percent error = |measured − true| ÷ |true| × 100. Use percent difference when neither value is the accepted one.