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Percent Error Calculator

Compare a lab measurement with the accepted value to get its percent error, or compare two measurements of equal standing to get their percent difference. Unlike a plain percentage change, both results are measures of disagreement, and this page keeps the two formulas apart.

What do you want to find?

Your experimental or estimated value.

The true, theoretical or reference value.

Result

Percent error

1.83%

The measured value is lower than the accepted value.

Error (measured − accepted)
-0.18
Absolute error
0.18
Signed percent error
-1.83%
Relative error
-0.0183486
Percent difference of the same two values
1.85%
Show the working
  1. Error = measured − accepted9.63 − 9.81 = -0.18
  2. Relative error = error ÷ |accepted|-0.18 ÷ |9.81| = -0.0183486
  3. Signed percent error = relative error × 100-0.0183486 × 100 = -1.83%
  4. Percent error = |signed percent error||-1.83%| = 1.83%

Percent error is usually reported without a sign. The signed version tells you whether the measurement came out high (+) or low (−).

Percent error or percent difference?

Both numbers tell you how far apart two values are as a percentage. The question is which value you trust.

  • Percent error is for when one value is known to be right, or is the agreed reference: a textbook constant, a manufacturer’s specification, a theoretical prediction. You divide by that accepted value, so the result says how far your measurement is from the truth, relative to the truth.
  • Percent difference is for when neither value is more trustworthy: two students’ results, two trials, two instruments. Picking either one as the yardstick would be arbitrary, so you divide by their average. Swapping the two values gives the same answer.

Choose the mode above, enter the two values, and the calculator shows the result with each step. In percent-error mode it also reports the signed error, so you can see whether the measurement came out high or low, and the percent difference of the same pair for comparison.

A percentage change is a third, different idea: how much a value grew or shrank from a starting point. For that, use the percentage calculator.

Formulas

Percent error = |measured − accepted| ÷ |accepted| × 100

Signed percent error = (measured − accepted) ÷ |accepted| × 100

Percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100

measured
the value you obtained (also called experimental or observed)
accepted
the reference value (also called true, theoretical or literature value)
a, b
two values of equal standing
| |
absolute value: drop any minus sign

For positive values the percent-difference denominator is simply the average (a + b) ÷ 2. Using the magnitudes keeps the result between 0% and 200% even when a value is negative. Percent error has no upper limit: a measurement three times the accepted value is 200% off.

Worked examples

Percent error. A pendulum experiment gives g = 9.63 m/s². The accepted value is 9.81 m/s².

  1. Error: 9.63 − 9.81 = −0.18 m/s² (the measurement is low)
  2. Relative error: −0.18 ÷ 9.81 = −0.0183486
  3. Percent error: 0.0183486 × 100 = 1.83% (signed: −1.83%)

Percent difference. Two trials measure 48 and 52 seconds.

  1. Difference: |48 − 52| = 4
  2. Average: (48 + 52) ÷ 2 = 50
  3. Percent difference: 4 ÷ 50 × 100 = 8%

Compare that with percent change: going from 48 to 52 is an 8.33% increase, but going from 52 to 48 is a 7.69% decrease. Percent difference avoids that asymmetry by not favouring either value.

Things to watch

  • An accepted value of zero can’t be used. Percent error divides by it. When the reference is 0 (a zero reading on a balance, a temperature of 0 °C), report the absolute error in the measurement’s units instead.
  • Scales with an arbitrary zero mislead. 21 °C against 20 °C is a 5% error, but the same temperatures in kelvin (294.15 and 293.15) give 0.34%. Use an absolute scale, or report the error in degrees.
  • Percent error is not uncertainty. It says how far one result landed from the reference, not how precise the method is. To describe the spread of repeated measurements, use the standard deviation calculator; to combine trials first, the average calculator.
  • Rounding. Keep full precision until the last step, then round the percentage to match the precision of your data.

Which one does my assignment want?

If the question gives a “true”, “theoretical”, “accepted” or “literature” value, it wants percent error. If it asks you to compare two of your own results, or yours with a lab partner’s, it wants percent difference.

Frequently asked questions

What is a good percent error?

There is no universal cut-off; it depends on the equipment and the experiment. In many school labs a few percent is reasonable, while precise instruments can reach well under 1%. Compare your result with the precision of your measuring tools rather than a fixed number.

Can percent error be negative?

The usual percent error uses the absolute value, so it is never negative. The signed percent error keeps the sign: negative when the measurement is below the accepted value and positive when it is above. The calculator shows both.

Can percent error be more than 100%?

Yes. Percent error has no upper limit. A measurement of 30 against an accepted value of 10 is off by 20, which is 200% of the accepted value. Percent difference, by contrast, never exceeds 200%.

Why is percent difference different from percent change?

Percent change divides by the starting value, so going from 48 to 52 (8.33%) and from 52 to 48 (−7.69%) give different answers. Percent difference divides by the average of the two values, 50 here, so both directions give 8%.

What if the accepted value is zero?

Percent error cannot be calculated because it divides by the accepted value. Report the absolute error, the plain difference in the measurement’s units, instead.

Last reviewed September 19, 2026