Percent Error Calculator

Worked example

Measuring gravity as 9.7 against the accepted 9.81 m/s² is a percent error of 1.12% — the measurement is 1.12% low, and the sign is worth keeping because a consistent bias points at the apparatus rather than at noise.

How to work it out yourself

1. 1.Put the accepted or published value in the second field. Percent error divides by the true value, so which number goes where changes the answer.
2. 2.Use percent difference instead when neither value is authoritative — comparing two instruments, or two measurements of the same unknown.
3. 3.Keep the sign while you are diagnosing. A run of errors all in one direction is a systematic problem; errors scattered either side are random.

The formula

1. Absolute error9.7 - 9.81
2. Percent errorabs(-0.11) / abs(9.81) * 100
3. Signed percent error-0.11 / abs(9.81) * 100
4. Percent difference, against the mean of the twoabs(-0.11) / ((abs(9.7) + abs(9.81)) / 2) * 100
5. Relative error as a fractionabs(-0.11) / abs(9.81)
6. Accuracy100 - 1.1213048

Source: NIST/SEMATECH e-Handbook of Statistical Methods — measurement error

Questions people actually ask

What is the difference between percent error and percent difference?

What they divide by. Percent error divides by the accepted value, so it needs one number to be the truth. Percent difference divides by the average of the two, and it is the right measure when neither is authoritative. Using percent error where you mean percent difference makes the answer depend on which value you happened to write second.

Should percent error be negative?

The conventional figure is absolute — the size of the error regardless of direction. The signed version is more useful while you are troubleshooting, because a consistent sign means a systematic bias: a scale reading low, a stopwatch started late, a thermometer with an offset. This page prints both.

What counts as an acceptable percent error?

It depends entirely on the field. School laboratory work often accepts under 5%; a machine shop works to fractions of a per cent; a calibration laboratory to parts per million. The number means nothing without the tolerance it is being judged against.

Why divide by the true value rather than the measurement?

Because the true value is the fixed reference — dividing by the measurement would make the error depend on the very thing being tested, and two experiments with different errors would not be comparable. It is also why percent error is undefined when the accepted value is zero.

Related

• Percentage Change CalculatorPercentage increase or decrease between two values, with the absolute difference and the multiplier.
• Confidence Interval CalculatorThe confidence interval around a sample mean, with the margin of error and what the interval does and does not claim.
• Rounding CalculatorA number rounded every way there is — half up, half to even, down, up and truncated — with the ones that disagree shown together.
• Percentage CalculatorWhat X% of a number is, plus the discounted price, the marked-up price and the remainder.
• Absolute Value CalculatorThe absolute value of a number, and the two solutions an equation of the form |ax + b| = c always has — which is the part a bare magnitude does not answer.
• Percent DifferencePercent difference between two values, divided by their mean — beside percent change, which divides by one of them and gives a different answer.

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