Percent Error Calculator — measured vs true value

How it works

Percent error tells you how accurate a measurement or estimate is, by comparing it with a known true value (also called the accepted or exact value). Take the size of the gap between them and express it as a percentage of the truth:

percent error = |measured − actual| ÷ |actual| × 100

The vertical bars mean absolute value — you drop the sign, so an overestimate and an underestimate of the same size give the same percent error. Dividing by the true value (not the measured one) is what makes it a fair, comparable measure of accuracy: the same 2-unit miss is minor against a true value of 100 but large against a true value of 10.

Worked example

Suppose you measure 105 but the true value is 100:

percent error = |105 − 100| ÷ |100| × 100 = 5 ÷ 100 × 100 = 5%

Measuring 48 against a true 50 gives |48 − 50| ÷ 50 × 100 = 2 ÷ 50 × 100 = 4% — and measuring 52 would give the same 4%, because only the size of the miss matters. A measurement of 9.7 for gravity when the accepted value is 9.81 m/s² is |9.7 − 9.81| ÷ 9.81 × 100 ≈ 1.12%.

Frequently asked questions

How do I calculate percent error?

Subtract the true value from the measured value, take the absolute value of that difference, divide by the true value, and multiply by 100. Measuring 203 when the true value is 200: |203 − 200| ÷ 200 × 100 = 1.5%.

Why divide by the true value and not the measured one?

Because percent error asks "how far off was I, relative to what's correct?" — so correctness is the reference. Using the true value keeps the measure consistent: two experiments aiming at the same true value can be compared directly, which wouldn't work if each divided by its own (different) measured result.

Why is percent error always positive?

Because of the absolute value in the numerator — it captures the magnitude of the error, not its direction. If you need to know whether you over- or under-estimated, use the signed relative error (measured − true) ÷ true, which is essentially the percent change from the true value to the measurement.

What does the true value being zero mean here?

Then percent error is undefined — you can't divide by zero, and there's no meaningful "percentage of nothing". When the accepted value is zero, report the absolute error (the plain difference) instead.

Is percent error the same as percentage difference?

No. Percent error compares a measurement against a known **true** value, so the denominator is that true value. Percentage *difference* compares two values neither of which is "correct", dividing by their average. Use percent error in experiments where one value is the accepted standard.

What counts as a good percent error?

It depends entirely on the field and the instrument — a 5% error might be fine for a rough physics lab but unacceptable in analytical chemistry or engineering. Percent error tells you the size of the discrepancy; whether it's acceptable is a judgement about the required precision, not something the number decides.