Percent error tells you how far an experimental result landed from the value it should have been, expressed as a percentage of that accepted value. It is the standard accuracy check in physics, chemistry and biology labs, and it is equally useful for comparing an estimate with the actual figure — a budget forecast against real spending, or a guessed weight against a scale reading.
How to use the percent error calculator
- Enter your measured value — the result from your experiment, survey or estimate.
- Enter the accepted value — the textbook constant, theoretical prediction or known true value.
- Choose absolute for the standard always-positive percent error, or signed if you need to show whether your result was high (+) or low (−).
- The tape shows the percent error, the raw error and the relative error; the steps show the calculation in the order a lab report expects.
Percent error formula
Drop the absolute-value bars in the numerator to get the signed version. The building blocks have their own names, which you may need in a report:
- Error (or absolute error): measured − accepted, in the original units.
- Relative error: the error divided by the accepted value, as a decimal.
- Percent error: the relative error times 100.
Worked example: measuring gravity
A class times a pendulum and calculates the acceleration due to gravity as 9.62 m/s². The commonly used accepted value is 9.81 m/s².
Error: 9.62 − 9.81 = −0.19 m/s²
Relative error: 0.19 ÷ 9.81 ≈ 0.019368
Percent error: 0.019368 × 100 ≈ 1.94%
Signed: −1.94%, meaning the measurement came out low
A note on the accepted value: the internationally defined standard acceleration of gravity is exactly 9.80665 m/s², but the real value varies with latitude and altitude from about 9.78 to 9.83 m/s². Using 9.80665 instead of 9.81 changes the answer slightly, to about 1.90%. Always state which accepted value you compared against.
Interpreting your result
A small percent error indicates accuracy — closeness to the true value. It says nothing about precision, which is how closely repeated measurements agree with each other. A scale that is miscalibrated by 2 grams can give the same wrong reading every time: very precise, consistently inaccurate. To judge precision, run several trials and look at their spread with the standard deviation calculator.
When you have several trials, compute the percent error of their average (the mean calculator helps) rather than averaging separate percent errors, which hides whether individual errors were high or low.
Where error comes from
- Systematic error pushes every result in the same direction: an uncalibrated instrument, a reaction-time delay when starting a stopwatch, heat lost to the surroundings. A signed percent error that is consistently negative or positive across trials hints at a systematic cause.
- Random error scatters results on both sides of the true value: small fluctuations in reading a scale or in air currents. It shrinks when you average more trials.
- Rounding of intermediate values can add error. Keep extra digits during calculations and round only the final answer to the correct number of significant figures.
Percent error vs. related measures
If you are comparing two measurements and neither is the accepted standard, use the percentage difference calculator, which divides by their average. If you need to know whether a part or reading falls inside an allowed band around a target, the percent tolerance calculator gives the minimum and maximum limits.
Frequently asked questions
What is the formula for percent error?
Percent error = |measured − accepted| ÷ |accepted| × 100. If you measure gravity as 9.62 m/s² and the accepted value is 9.81 m/s², the percent error is 0.19 ÷ 9.81 × 100 ≈ 1.94%.
Can percent error be negative?
The usual definition takes the absolute value, so percent error is never negative. Some instructors ask for a signed percent error, where a negative result means your measurement was too low and a positive result means it was too high.
What is a good percent error?
It depends on the experiment and the equipment. In many introductory lab courses, results within about 5% are considered good, but precise instruments may be expected to land under 1%, while rough field estimates can be acceptable at 10% or more. Follow the standard set by your instructor or method.
What is the difference between percent error and percent difference?
Percent error compares a measurement against a known, accepted value and divides by that value. Percent difference compares two measurements when neither is known to be correct, and divides by their average.
Why can't the accepted value be zero?
Percent error divides by the accepted value, and dividing by zero has no answer. When the true value is zero, report the absolute error in the measurement's units instead.