Percentage Error Calculator
See how far a measured value is from the accepted value, as a percentage — and as a raw absolute error.
Two values in
Enter what you measured and the accepted true value; the calculator returns both the percent and absolute error.
True value can't be zero
Percent error divides by the true value, so it is undefined when that value is zero.
What is percentage error?
Measured versus accepted, as a percentage
Percentage error tells you how far a measured (observed) value lies from the accepted, true, or theoretical value, expressed as a percentage of that true value. It is the standard way scientists, engineers, and students quantify the accuracy of a measurement: the smaller the percent error, the closer the measurement is to the value it should have produced. Because it scales the gap by the true value, it lets you compare the accuracy of measurements taken at completely different magnitudes.
The calculation has three short steps wrapped into one expression.
percent error = |observed − true| ÷ |true| × 100The vertical bars mean absolute value, which discards the sign so the error is reported as a positive magnitude whether you measured too high or too low. Dividing by the absolute true value turns the raw gap into a fraction of what the answer should be, and multiplying by 100 converts that fraction into a percentage.
You measure the acceleration due to gravity as 9.8 m/s², and the accepted value is 9.81 m/s².
Find the absolute error
|9.8 − 9.81| = 0.01.Divide by the true value
0.01 ÷ 9.81 ≈ 0.00102.Convert to a percentage
0.00102 × 100 ≈ 0.10%.Interpret it
A 0.10% error is very small — the measurement is extremely close to the accepted value.
Both numbers describe the same gap, but they answer different questions.
Absolute error
The raw size of the gap, |observed − true|, in the original units. Useful when the scale is fixed and familiar.
Percentage error
The gap as a share of the true value. Lets you compare accuracy across measurements of very different sizes.
Context decides
A "good" percent error depends on the field — under 5% in a school lab, far tighter in precision work.
An absolute error of 1 unit is enormous when the true value is 2 but negligible when it is 1,000. Percentage error makes that difference explicit, which is why lab reports and quality checks usually quote it.
Read the percent error against the tolerance expected for your task. In an introductory physics or chemistry lab, a result under a few percent usually indicates a well-run experiment, while a double-digit percent error points to a systematic problem — a miscalibrated instrument, a misread scale, or a flawed method — rather than ordinary random noise. If you are comparing two measurements where neither is the accepted reference, you want percent difference instead. For the reverse problem — recovering an original amount after a percentage change — try our reverse percentage calculator.
Percent error is simple, which is both its strength and its limit.
It needs a trusted reference value
Percentage error only makes sense when you have an accepted true value to compare against, and it is undefined when that value is zero. It reports magnitude, not direction, so it does not tell you whether you measured high or low unless you track the sign yourself. It also says nothing about precision or repeatability — a measurement can have a small percent error by luck while still being unreliable. Use it alongside, not instead of, a proper uncertainty analysis.