Home ›
Math › Percent Error Calculator
· 🌐 EN / DE Percent Error Calculator
Compare a measured value against the accepted true value to find the percent error.
Example
A student measures the boiling point of water as 9.8 (observed) when the accepted true value is 10.
percent error = |9.8 - 10| / |10| x 100
= 0.2 / 10 x 100
= 2%The measurement is a 2% underestimate.
How it works
Enter the observed (measured) value and the true (accepted) value. Percent error is computed as |observed - true| / |true| x 100.
Good to know
This Percent Error Calculator compares a measured (observed) value against the accepted true value and instantly returns the percent error along with the absolute error, the signed error, and the direction of the deviation. It's built for students in chemistry, physics, and lab courses, as well as engineers, QA technicians, and anyone checking how far a reading strays from a reference standard.
Reach for it whenever you've taken a measurement and want to know how accurate it was: a titration result versus the theoretical concentration, a gravity experiment versus 9.81 m/s², a sensor reading versus a calibrated standard, or an estimate versus a known answer. Type your observed value and the true value, and the four outputs update as you type.
Read the results together rather than in isolation. The percent error tells you relative accuracy as a fraction of the true value, the absolute error is the raw gap in your original units, and the signed error plus direction label show whether you read high (overestimate, positive) or low (underestimate, negative). A small percent error on a large quantity can still mean a sizeable absolute gap, so the sign and magnitude matter for diagnosing what went wrong.
One caveat to keep in mind: percent error divides by the true value, so if your accepted value is zero the result is mathematically undefined and the tool will say so. In that case, rely on the absolute or signed error instead. Also make sure you put the values in the right boxes, since swapping observed and true changes the denominator and gives a different percentage.
Frequently asked questions
What is the formula for percent error?
Percent error = |observed - true| / |true| x 100, where observed is your measured value and true is the accepted/expected value. The absolute value makes the result non-negative.
Why does this show 'undefined' for percent error?
Percent error divides by the true value, so when the true value is 0 the calculation is undefined. Use a non-zero accepted value, or report absolute error instead.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is a good percent error in a chemistry or physics lab?
There is no universal cutoff, but many introductory lab courses treat results under about 5% as good and under 10% as acceptable, depending on the equipment and experiment. Precision instruments and professional settings often demand far tighter tolerances, so always check your assignment or standard for the expected range.
What is the difference between percent error and percent difference?
Percent error compares a measured value to a known accepted (true) value and divides by that true value. Percent difference compares two experimental values when neither is treated as correct, dividing by their average instead.
Can percent error be greater than 100%?
Yes. If your measured value is more than double the true value, or the true value is very small relative to the error, the percent error can exceed 100%. This usually signals a large mistake in measurement or in which value you treated as the reference.
Is percent error always positive?
The standard percent error formula uses absolute value, so it is reported as a non-negative number. To capture whether you measured too high or too low, look at the signed error and direction label, which show the deviation with its plus or minus sign.
How do you calculate percent error by hand?
Subtract the true value from the observed value, take the absolute value of that difference, divide by the absolute value of the true value, then multiply by 100. For example, |9.8 - 10| / |10| x 100 equals 2%.
What does percent error tell you about accuracy versus precision?
Percent error measures accuracy, meaning how close a single result is to the true value. It does not measure precision, which is how closely repeated measurements agree with each other; you would assess precision using the spread or standard deviation of multiple trials.
What causes a high percent error in an experiment?
Common causes include systematic errors like uncalibrated or biased instruments, random errors from reading or timing, environmental factors such as temperature, and procedural mistakes. A consistently high or low signed error often points to a systematic source rather than random noise.
Related calculators