Percent Error Calculator
Calculate percent error between a measured (experimental) value and the accepted (theoretical) value.
- Theoretical (Accepted)10
- Experimental (Measured)9.8
Your measured value is off from the accepted value by 2% — the closer the two bars, the more accurate the measurement.
ƒShow your work
- 1|9.8 − 10| ÷ |10| × 100 = 2%
About the Percent Error Calculator
Percent error is the standard way science classes and labs express how far a measured (experimental) result strayed from the accepted (theoretical) value — a student measuring gravitational acceleration and getting 9.7 m/s² instead of the accepted 9.8, or a chemistry class weighing a reaction product against the yield predicted on paper. It turns a raw difference into a percentage, which makes it comparable across completely different kinds of measurements and different scales of the same measurement.
It's used constantly in lab reports specifically because a raw difference like '0.2 off' means very little on its own — 0.2 off of a value near 10 is a big deal, while 0.2 off of a value near 10,000 barely registers. Percent error puts the discrepancy on a consistent scale, and that scale is what actually gets judged against a class's or lab's accuracy expectations.
How it’s calculated
The formula is %Error = |experimental − theoretical| / |theoretical| × 100. Subtract the theoretical (accepted) value from the experimental (measured) one, take the absolute value so the sign doesn't matter, divide by the absolute value of the theoretical value to put it on a relative scale, and multiply by 100 to express it as a percentage.
Using the absolute value matters because percent error is meant to describe the size of the discrepancy, not its direction — a measurement that's too high and one that's too low by the same relative amount get the same percent error. If direction matters for your write-up, that's usually reported separately as 'measured high' or 'measured low' alongside the number.
Frequently asked questions
What counts as a good percent error?
It depends entirely on the experiment and the precision of the equipment involved — there's no universal cutoff. In an introductory physics lab, under 5% is often considered solid; in high-precision scientific work, even a fraction of a percent might be flagged as too high.
Why does the percent error formula use absolute value?
So the result reflects the size of the discrepancy regardless of whether the measured value came in too high or too low. Without the absolute value, a measurement that's too low would produce a negative percentage, which is awkward to interpret as an 'error size.'
What's the difference between percent error and percent difference?
Percent error compares a measured value against a known, accepted 'true' value (used when you're testing accuracy against theory). Percent difference compares two measured values against each other with neither treated as the accepted standard (used when comparing two experimental trials, for instance).
Can percent error be negative?
Not with the standard formula, since it uses absolute value in the numerator — the result is always zero or positive. If a version of the formula omits the absolute value, a negative result just means the experimental value came in below the theoretical one.
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