How percent error is calculated
Percent error is the standard way science and engineering express how far a measured result strays from the accepted or theoretical value, scaled to a percentage so results of different sizes can be compared.
- true — the accepted or theoretical value
- measured — the experimental or observed value
More detail
Why the true value is in the denominator
Percent error scales the absolute error against the true value, not the measured one — a 5-unit error means something very different for a true value of 10 (50% error) versus 1,000 (0.5% error). Dividing by |true| keeps the sign of the true value from flipping the result, so percent error is always reported as a non-negative figure.
Absolute error vs. percent error
Absolute error keeps the original units (e.g. 5 grams, 5 volts) and shows the raw size of the gap. Percent error strips the units and expresses that same gap as a share of the true value, which is what makes it useful for comparing the precision of measurements taken at very different scales.
Reading the result. A percent error under about 5% is generally considered good for typical classroom or lab experiments, but the acceptable threshold depends entirely on the field and instrument — check your assignment or protocol rather than relying on a universal cutoff.
Frequently asked questions
What is the percent error if the true value is 100 and the measured value is 95?
Absolute error = |95 − 100| = 5. Percent error = 5 / |100| × 100 = 5%. Enter true value 100 and measured value 95 above to see both results computed live.
How do you calculate percent error?
Take the absolute value of (measured − true), divide by the absolute value of the true value, then multiply by 100: |measured − true| / |true| × 100. The true value goes in the denominator, not the measured value.
Why is percent error always positive?
Because the formula uses the absolute value of the difference, |measured − true|, before dividing. This means percent error reports how far off a measurement is, not whether it overshot or undershot the true value.
What happens if the true value is 0?
Percent error is undefined, since the formula divides by |true value|. The calculator shows "—" for both results in that case; compare the raw difference by hand instead.
What's a "good" percent error?
There's no universal number — it depends on the field, instrument precision, and what's being measured. Many introductory science labs treat under ~5% as reasonable agreement, but always check the specific standard or rubric you're working against.