Percent Error Calculator
Calculate the percent error between measured and accepted values, for a single measurement or a full set of trials
By Waqar Mushtaq · Last updated:
Percent error measures how far a measured or estimated value is from the accepted (true) value, as a percentage of that accepted value. It's the standard accuracy figure in science lab reports -- measuring gravitational acceleration, a boiling point, a density, or a reaction yield and comparing it to the textbook value. Enter a single measurement, or paste in several trials at once: the calculator then shows each trial's error, which trial landed closest, the percent error of the mean, and the average error per trial, along with whether your measurements ran high or low.
How Percent Error Is Calculated
O(n) in the number of trialsV_measured = your experimental value · V_accepted = the known or theoretical value
Subtract the accepted value from the measured value, take the absolute value, divide by the accepted value, and multiply by 100.
Example: you measure gravitational acceleration as 9.6 m/s², and the accepted value is 9.81 m/s².
- Absolute error: 9.6 − 9.81 = −0.21 m/s²
- Percent error: |−0.21| / 9.81 × 100 = 2.14% (the measurement was low)
Signed percent error. Leaving out the absolute value bars gives a signed result: negative means the measurement was below the accepted value, positive means above. Many chemistry courses ask for this form because the direction hints at the source of error (for example, a percent yield above 100% usually means the product wasn't fully dried). This calculator reports both.
Several trials. With multiple measurements, two summary numbers are useful and they answer different questions:
- Percent error of the mean -- how accurate the set is on average. Trials that overshoot and undershoot partly cancel out, so this can be small even when individual trials are scattered.
- Average error per trial -- how far a typical single trial landed from the accepted value.
For trials of 9.6, 9.9, 9.75, and 10.1 against 9.81, the mean (9.8375) is only 0.28% off, but the average trial is 1.66% off.
Percent error is undefined when the accepted value is 0. If there's no accepted value at all and you're comparing two measurements, use the Percent Difference Calculator instead.
Use Cases
Physics and Chemistry Lab Reports
Report the accuracy of a measured constant (g, the speed of sound, a specific heat, a molar mass) against the accepted value, for one trial or an averaged set.
Percent Yield Sanity Checks
Compare an actual yield to the theoretical yield and see whether it came in high or low -- a yield above theoretical is a signal that something (water, impurities) is inflating the mass.
Instrument Calibration
Check a scale, thermometer, or meter against a reference standard and confirm the reading is within the manufacturer's stated accuracy (for example, ±0.5%).
Forecast and Estimate Accuracy
Measure how close a budget estimate, sales forecast, or engineering estimate came to the actual outcome once it's known.
Frequently Asked Questions
Can percent error be negative?
The standard formula uses the absolute value, so percent error is zero or positive. Some courses use a signed version without the absolute value -- negative when the measurement is below the accepted value, positive when above. This calculator shows both.
What is a good percent error?
It depends on the experiment and the equipment. In introductory lab courses, results within about 5% are often considered good and within 10% acceptable, but precise instruments and well-controlled experiments can achieve well under 1%. Your instructor or the instrument's rated accuracy is the real benchmark.
What is the difference between percent error and percent difference?
Percent error compares a measurement to a known accepted value and divides by the accepted value. Percent difference compares two values when neither is known to be correct, and divides by their average.
Should I average my trials before or after calculating percent error?
Both are common and they measure different things. Averaging first and then computing the error of the mean tells you how accurate the set is overall. Computing each trial's error and averaging those tells you how far individual trials typically miss. The calculator shows both when you enter multiple trials.
Why is percent error undefined when the accepted value is 0?
The formula divides by the accepted value, and division by zero is undefined. For a true value of 0, report the absolute error (measured − accepted) in the measurement's units instead.
Methodology
The formula above is implemented as a standalone module covered by unit tests, so its worked examples are re-checked on every change to the site. It is verified against the authoritative sources listed below.
Maintained by Waqar Mushtaq. Spotted a result that looks wrong? Report it and it becomes a failing test.