Math · Lab calculations
Percent error calculator.
Compare what you measured with the accepted (true, theoretical or literature) value to get percent error, or switch to percent difference when you have two measurements and neither is the reference. Choose how many significant figures to show. Runs in your browser; nothing is sent.
You measured 8.2 and the accepted value is 9.81: percent error = |8.2 − 9.81| ÷ 9.81 × 100 = 1.61 ÷ 9.81 × 100 = 16.41%, with your value below the accepted one. For two measurements, 50 and 60 differ by 10 against their mean of 55, a percent difference of 18.18%.
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The formulas
Percent error = |measured − accepted| ÷ |accepted| × 100. It scales the error by the accepted value, so the accepted value must not be 0. The absolute value means the answer is never negative; this calculator also says whether your value was above or below the accepted one. Percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100. It divides by the average of the two values, so swapping them gives the same answer, which is what you want when neither is more correct than the other, such as two trials of the same experiment.
Which one should I use?
Use percent error when one number is the reference: a textbook value, a standard, a calculated theoretical yield. Use percent difference when you compare two measurements of equal standing. For the change from an old value to a new one, such as a price rise, use the percent increase and decrease calculator, which divides by the starting value. Some courses define percent difference differently, for example relative to one chosen value, so check which formula your instructor expects.
Worked examples
Percent error: a student measures 8.2 where the accepted value is 9.81. The error is |8.2 − 9.81| = 1.61, and 1.61 ÷ 9.81 = 0.16412, so the percent error is 16.41% (to 4 significant figures), and the measured value is below the accepted one. If you swap them, measured 9.81 against accepted 8.2, the answer changes to 19.63%, because the denominator changes. Percent difference: 50 and 60 differ by 10, their mean is 55, and 10 ÷ 55 = 0.18182, so the percent difference is 18.18%, the same whichever order you enter them.
Reporting the answer
Quote percent error to the precision your lab or instructor asks for; the significant figures box lets you match it, and the number of figures should not exceed what your measurement supports (see the significant figures calculator). Percent error describes how far off a result is from a reference; it is not the same as the uncertainty of the measurement, which the uncertainty calculator handles.
Sources, opened 8 October 2026: Wikipedia, Approximation error (percent error as 100% times the absolute value of (v − vapprox) / v, with v the true value); Wikipedia, Relative change (percent error as a special case of relative change in measurement, and the symmetric difference |x − y| / ((|x| + |y|) / 2) based on the arithmetic mean).
Note: Educational calculator. Percent error against a reference is not a measurement uncertainty. Follow your instructor’s formula and rounding convention.
Frequently asked questions
How do you calculate percent error?
Subtract the accepted value from your measured value, take the absolute value, divide by the accepted value and multiply by 100. For a measured 8.2 against an accepted 9.81, that is 1.61 / 9.81 x 100 = 16.41%.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known accepted value and divides by that value. Percent difference compares two values that have equal standing and divides by their average, so the order does not matter.
Can percent error be negative?
The usual formula uses the absolute value, so it is positive. Dropping the absolute value gives a signed error that is negative when your measurement is below the accepted value. This calculator reports the direction separately.
What if the accepted value is zero?
Percent error is undefined because it divides by the accepted value. Report the absolute error instead.
What is a good percent error?
It depends on the experiment and the instrument. There is no universal cutoff, so use the limit your instructor or method gives. As a common rule of thumb, not a published standard, a percent error much larger than your estimated measurement uncertainty suggests a systematic mistake.
Is percent error the same as relative error?
Percent error is relative error written as a percentage. Relative error is the absolute error divided by the accepted value, so 0.1641 as a relative error is 16.41% as a percent error.