Absolute & Relative Error Calculator

Math Updated 16 Jun 2026

This absolute and relative error calculator compares a measured value with the true (actual) value to quantify how far off a measurement is. Enter your measured value M and the actual value A, and it returns the absolute error |M − A|, the relative error as a percentage, the resulting accuracy, and whether you over- or under-estimated.

Formula

Absolute Error = |M − A| · Relative Error = |M−A|/|A| · Accuracy = (1 − RE) × 100%
  • Absolute error is the size of the gap between your measurement and the true value: |M − A|. It carries the same units as the quantity.
  • Relative error scales that gap by the true value: |M − A| / |A|, usually expressed as a percentage. It is unitless, so you can compare errors across different magnitudes.
  • Percent accuracy is (1 − relative error) × 100%, so a small relative error means high accuracy.
  • The signed difference M − A shows direction: positive means you overestimated, negative means you underestimated.
  • The actual value A cannot be zero, because relative error divides by |A|.

Example Calculation

Inputs
  • Measured Value: 98.5
  • Actual (True) Value: 100

With a measured value of 98.5 and an actual value of 100, the absolute error is |98.5 − 100| = 1.5. The relative error is 1.5 / 100 = 1.5%, giving 98.5% accuracy, and because 98.5 < 100 the measurement is underestimated.

Frequently asked questions

What is the difference between absolute and relative error?
Absolute error |M − A| is the raw size of the gap in the original units. Relative error divides that by the true value, |M − A| / |A|, so it is a unitless fraction or percentage you can compare across measurements.
How do I calculate absolute error?
Subtract the actual value from the measured value and take the absolute value: absolute error = |M − A|.
Why can't the actual value be zero?
Relative error divides by the actual value, |M − A| / |A|. If A is zero that division is undefined, so the calculator requires a non-zero actual value.
What does percent accuracy mean here?
It is (1 − relative error) × 100%. An accuracy of 98.5% means the measurement is within 1.5% of the true value.
Is relative error the same as percent error?
Yes. Percent error is just the relative error expressed as a percentage, i.e. relative error × 100%.