Percent Error Calculator
Compare a measured (observed) value against the accepted true value and get the percent error with every step shown — absolute error, relative error, and both the unsigned and signed conventions used in lab reports.
What percent error tells you
Percent error measures how far a measurement strays from the accepted value, scaled to the size of that value — being off by 5 grams matters far more when weighing 20 grams than 20 kilograms. A small percent error suggests your method and instruments are sound; a large one points to a systematic problem such as a calibration offset, unit mix-up, or flawed technique. The sign (when kept) tells direction: negative means you measured low, positive means high.
How it’s calculated
Absolute error = |observed − true|. Relative error = absolute error ÷ |true|. Percent error = relative error × 100%. The signed variant skips the absolute value in the numerator: (observed − true) ÷ true × 100%.
Percent error is undefined when the true value is 0. Results update as you type and are rounded to 4 significant figures for display.
Worked example
A student measures a density of 56.891 against an accepted 62.327. Absolute error = |56.891 − 62.327| = 5.436. Divide by the true value: 5.436 ÷ 62.327 = 0.08722. Multiply by 100 for a percent error of 8.722%; kept signed it is −8.722%, meaning the measurement ran low. Similarly, observing 7 when the truth is 9 gives a signed error of −22.22%.
Common mistakes
- Dividing by the observed value instead of the true value — the accepted value always goes in the denominator.
- Mixing units between the two values (grams vs kilograms) before comparing.
- Reporting a negative “percent error” when the assignment expects the absolute-value convention — check which your course uses.
- Confusing percent error with percent difference or percent change, which use different denominators.
Where it is used
- Chemistry and physics lab reports comparing measurements to accepted constants.
- Quality control, checking parts against specification values.
- Forecast accuracy — comparing an estimate to the actual outcome.
- Calibrating instruments against reference standards.
Frequently asked questions
What is the percent error formula?
Percent error = |observed − true| ÷ |true| × 100%. Take the difference between your measurement and the accepted value, divide by the accepted value, and express it as a percentage. An observed 56.891 against a true 62.327 gives 5.436 ÷ 62.327 × 100 = 8.72%.
Can percent error be negative?
With the standard absolute-value formula, no — it is always zero or positive. Some teachers and labs drop the absolute value to keep the sign: negative then means you measured low, positive means you measured high. This calculator reports both conventions.
What is a good percent error?
It depends on the field. School chemistry and physics labs often accept under 5–10%; engineering tolerances can demand under 1%; rough field estimates may tolerate more. A very large error (say 50%+) usually signals a mistake in method, units, or arithmetic rather than instrument noise.
What is the difference between percent error and percent difference?
Percent error compares a measurement against a known true value. Percent difference compares two measurements of equal standing, dividing by their average instead of a true value. Use percent error only when an accepted reference value exists.
What if the true value is zero?
Percent error is undefined when the true value is zero because you cannot divide by zero. In that case report the absolute error alone, or use a different accuracy metric appropriate to the experiment.