Percent Error Calculator

Find percent error from a measured and a true value, with signed, absolute and relative error, or analyse several trials for accuracy and precision.

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About this tool

What is the Percent Error Calculator?

Percent error tells you how far a measurement landed from the value it should have been, as a share of that true value. Type what you measured and the accepted value, and the calculator returns the percent error, the signed percent error (which shows whether you were high or low), the absolute error in your own units and the relative error as a plain fraction.

Lab classes rarely stop at one reading, so a second mode takes a list of trials. It reports the percent error of the mean, the mean of the individual percent errors and the relative standard deviation of the set. Those three numbers separate accuracy, how close the average is to the truth, from precision, how tightly the trials agree.

The arithmetic is done with exact fractions rather than floating point, so 9.81 against 9.8 comes out as exactly 5/49 percent and the only rounding is the number of decimal places you pick for the headline figure.

  • Percent, signed percent, absolute and relative error at once
  • Trials mode with mean, percent error of the mean, MAPE, sample SD and RSD
  • Exact fraction arithmetic with your choice of decimal places
  • Worked steps you can copy into a lab report
  • Runs in your browser with a shareable link
Read the guide: How to Calculate Percent Error (and What It Does Not Tell You)

How to use the Percent Error Calculator

  1. Choose One measurement for a single reading or Several trials for a set of repeated readings.
  2. Type the measured (experimental) value and the true (accepted or theoretical) value. Decimals, negatives, fractions and E notation all work.
  3. Read the percent error. The signed figure below it is negative when your measurement was below the true value.
  4. Set the number of decimal places to match your report. The exact value stays visible underneath.
  5. In trials mode, paste your readings one per line and compare the percent error of the mean (accuracy) with the relative standard deviation (precision).

Worked examples

Measuring g with a pendulum

Input

Measured 9.6 m/s², true 9.81 m/s²

Output

2.141% (signed −2.141%)

The error is 0.21 m/s², and 0.21 / 9.81 = 0.02141, so the reading is about 2.1% low.

Density of aluminium

Input

Measured 2.65 g/cm³, true 2.70 g/cm³

Output

1.852%

The units cancel in the division, so percent error has no unit even though the absolute error is 0.05 g/cm³.

A negative true value

Input

Measured −10.5 °C, true −10 °C

Output

5% (signed −5%)

Dividing by |−10| keeps the percent error positive; the signed form shows the reading was colder, that is lower, than expected.

Five trials of g

Input

9.79, 9.82, 9.85, 9.76, 9.80 against 9.80665

Output

Percent error of the mean about 0.027%

The individual trials miss by up to 0.48%, but they scatter on both sides, so their average lands almost exactly on the true value.

Background and insight

The standard definition is percent error = |measured − true| / |true| × 100. The vertical bars are absolute values: the top one makes the error a distance, and the bottom one keeps the percentage positive when the true value is negative, such as a temperature below zero. Some teachers and lab manuals drop the top bars and report a signed percent error, (measured − true) / |true| × 100, so that a minus sign means the measurement was low. Both appear on the page so you can copy whichever your course asks for.

Percent error assumes one of the two numbers is the reference: a defined constant, a value from a data book, or the result of a more precise method. When neither number has that status, for example two students comparing their own readings, percentage difference is the fairer measure because it divides by the average of the two. That is a different calculation, available on the Percentage Calculator.

In metrology the word "error" has a strict meaning: the measured value minus the true value. The international Guide to the Expression of Uncertainty in Measurement (GUM, JCGM 100) points out that the true value is never known exactly, which is why careful reports pair an error estimate with an uncertainty. A percent error near zero is good news, but it does not prove a method is precise, and a run of trials with a small relative standard deviation can still be biased by a systematic error. The trials mode is built to show that difference.

Common use cases

  • Physics and chemistry lab reports

    Compare a measured constant, yield or concentration with the accepted value and report the percent error with the sign your teacher expects.

  • Instrument calibration checks

    Read a reference weight, voltage or gauge block and see whether the instrument is inside its stated tolerance as a percent of reading.

  • Estimates against actuals

    Check how far a cost, time or sales estimate was from the actual figure, and whether you tend to guess high or low.

  • Repeated measurements

    Paste a column of trials to see accuracy and precision side by side, which is the usual structure of a lab error analysis section.

Tips and limitations

  • Percent error is undefined when the true value is zero. Report the absolute error instead.
  • Do not round the measured value before calculating. Round the final percent error, usually to two or three significant figures.
  • A small percent error of the mean with a large relative standard deviation means random scatter that happened to average out; take more readings before trusting it.
  • If both numbers are your own measurements, use percentage difference, not percent error.
  • Percent error above 100% is possible: measuring 25 when the true value is 10 gives 150%.

Frequently asked questions

What is the formula for percent error?

Percent error = |measured − true| / |true| × 100. Subtract, take the absolute value, divide by the size of the true value and multiply by 100. Measuring 9.6 when the true value is 9.81 gives 0.21 / 9.81 × 100 = 2.14%.

Can percent error be negative?

With the standard formula, no: the absolute value makes it positive. Many courses also use a signed percent error, (measured − true) / |true| × 100, which is negative when the measurement is too low. The calculator shows both.

Which value goes on the bottom?

Always the true, accepted or theoretical value. Dividing by your measurement instead gives a different and non-standard answer, and the two diverge as the error grows.

What is a good percent error?

It depends on the experiment and the equipment. School labs often treat under 5% as acceptable and under 1% as very good, but a calibrated instrument may be specified to 0.1% or better. Compare against the tolerance or uncertainty that applies to your method rather than a universal cut-off.

How is percent error different from percent difference?

Percent error compares a value with a trusted reference. Percent difference compares two values of equal standing, dividing their gap by their average, so it gives the same answer whichever number you list first.

How do I find percent error for several trials?

Average the trials and compute the percent error of that mean. The trials mode does this and also gives the mean absolute percent error (the average of each trial's own error) and the relative standard deviation, which measures how much the trials scatter.

What is relative error?

Relative error is the absolute error divided by the size of the true value, left as a fraction or decimal. Percent error is the same number multiplied by 100.

Why is my percent error over 100%?

Because the miss is larger than the true value itself. If the true value is 10 and you measured 25, the error of 15 is 150% of 10. Check units and decimal points first; a factor-of-ten slip is the usual cause.

Is there an in-depth guide to the Percent Error Calculator?

Yes. “How to Calculate Percent Error (and What It Does Not Tell You)” covers the background, how it works, common pitfalls and worked examples. Read the full guide.

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