What is the percent error formula?

Percent error equals the absolute difference between measured and accepted values divided by the absolute accepted value, multiplied by 100.

Can percent error be negative?

The standard percent error is nonnegative. Use signed relative error when you need to show whether the measurement is over or under the accepted value.

What if the accepted value is zero?

Percent error is undefined when the accepted value is zero. Use absolute error or another method-approved baseline.

Percent Error Calculator

Calculate percent error between a measured or experimental value and an accepted value, with absolute error, signed relative error, and direction.

Measured / Experimental Value

Actual / Accepted Value

Percent error shows how far a measured result is from a known accepted value. Use it for lab work, physics, chemistry, measurement checks, and approximations.

Percent error is shown as the magnitude of the deviation; direction is shown separately. If the accepted value is uncertain, check the measurement method and reference source.

What percent error measures

Percent error compares a measured, experimental, observed, or approximate value with an accepted reference value. Use it when one value is the standard and the other is the measurement being checked.

Measured value: the result from an experiment, observation, forecast, or approximation.
Accepted value: the known, theoretical, true, or reference value.
Percent error: the magnitude of the relative error expressed as a percent.
Signed relative error: the direction, showing over or under the accepted value.

Percent error formula

E_{ab s} = ∣ m - a ∣

E_abs is absolute error, m is measured value, and a is accepted value.

P_{er r or} = \frac{∣ m - a ∣}{∣ a ∣} \cdot 100%, a \neq = 0

P_error is percent error. The accepted value a must not be zero.

E_{s i g n e d} = \frac{m - a}{∣ a ∣} \cdot 100%

E_signed is signed relative error; positive means over and negative means under.

Percent error vs percent difference

Metric	Use when
Percent error	One value is accepted or theoretical
Percentage difference	Both values are peer measurements
Percentage change	There is an old value and a new value

If the accepted value is zero, percent error is undefined because the formula divides by the accepted value. Use absolute error or a method-approved reference instead.

Frequently Asked Questions

Sources and References

Calculations are based on the listed reference sources. Links open in a new tab.

Updated: June 2, 2026

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