Percent Error Calculator with Sig Figs

How to use the percent error calculator

Type your measured value (the experimental result) and the accepted value (the true, theoretical or textbook value). Decimals, negative numbers and scientific notation all work: 1.23e-4, 1.23E-4 and 1.23 x 10^-4 are the same number.
Pick how to round the answer: 2 decimal places, or significant figures following the rule below.
Read the percent error, the absolute and relative error, the signed error and the answer with significant figures. The working is shown under the result.

To compare two of your own measurements when there is no accepted value, choose Percent difference.

Percent error formula

A LibreTexts chemistry text defines percent error as the absolute value of the error, divided by the accepted value, and multiplied by 100%. As a formula:

percent error = |measured - accepted| / |accepted| x 100

The calculator also shows the two parts that go into it. The absolute error is |measured - accepted|, in the same units as your values. The relative error is that divided by |accepted|, a plain number. Percent error is the relative error times 100. The accepted value is written inside bars here so the answer stays positive when the accepted value is negative, such as a temperature below zero.

How to calculate percent error

Subtract the accepted value from the measured value.
Drop the minus sign, if there is one.
Divide by the accepted value.
Multiply by 100 and add the % sign.

The LibreTexts worked example compares a measured density of aluminum of 2.45 g/cm³, the value used in its working, with an accepted 2.70 g/cm³. Press Try an example to see it in the calculator.

Step	Working	Result
Difference	2.45 - 2.70	-0.25
Absolute error	\|-0.25\|	0.25
Relative error	0.25 / 2.70	0.0926
Percent error	0.0926 x 100	9.26%

Negative percent error

Percent error is usually reported without a sign. The signed version keeps it: (measured - accepted) / |accepted| x 100. The same LibreTexts page notes: If the experimental value is less than the accepted value, the error is negative. Reporting the absolute value is common, it adds, to avoid the confusion of a negative error. The aluminum example has a signed error of -9.26%: the measurement came out low. Use the sign when it matters which way your result missed, for example when you suspect product was lost.

Percent error calculator with sig figs

Choose Significant figures and the answer is rounded to the figures your values support. The calculator counts them with these rules from a LibreTexts chemistry course: All nonzero digits are significant. Zeros between them count, leading zeros do not, and trailing zeros are significant only if the number has a decimal point. So 50 has one significant figure and 50. has two. In scientific notation only the digits before the power of ten count: 6.0 x 10^-5 has two.

Percent error has two steps, and each has its own rule. For subtraction, the answer gets the same number of decimal places as the term with the fewest decimal places. For division, limit the significant figures in the answer to the lowest count. The calculator counts the figures in the difference at the shared decimal place, takes the lower of that and the accepted value's count (the 100 is exact), and rounds only the final answer, halves up.

Measured	Accepted	Difference	Unrounded	Sig figs
2.45 g/cm³	2.70 g/cm³	0.25 (2 figures)	9.2593%	9.3%
9.6 m/s²	9.81 m/s²	0.21, kept as 0.2 (1 figure)	2.1407%	2%
6.15 x 10^23	6.022 x 10^23	0.128 x 10^23, kept as 0.13 x 10^23 (2 figures)	2.1255%	2.1%

Many classes simply give the answer the figures of the inputs, which would report the first row as 9.26%, as the LibreTexts example does. The step by step rule gives 9.3%, because 2.45 - 2.70 = 0.25 has only two significant figures. Both are shown, so use the one your teacher asks for.

Percent error in chemistry and physics labs

In chemistry, the accepted value is often a density, a molar mass, a theoretical yield or a constant. NIST gives the Avogadro constant as exactly 6.022 140 76 x 10^23 per mole; the third row above rounds it to 6.022 x 10^23. In physics labs it is often the acceleration due to gravity, a known resistance or the speed of sound. Type the value you were told to use.

Percent error only makes sense on a scale that starts at a true zero. A 1 degree miss is 1% of 100 °C but 100% of 1 °C, so for temperatures compare in kelvin, or report the absolute error.

Percent error vs percent difference

A physics lab manual from NC State University and WebAssign draws the line clearly. Use percent error when you compare an experimental result to a value determined by theory or to an accepted known value. Use percent difference when both values come from experiment and there is no accepted value. Percent difference divides by the average of the two:

percent difference = |first - second| / ((first + second) / 2) x 100

Two trials giving 0.92 and 1.00 g/mL differ by 0.08 and average 0.96, so the percent difference is 0.08 / 0.96 x 100 = 8.33%. Neither value is treated as the right one, which is why the average is used.

Percent error in Excel or Google Sheets

With the measured value in B2 and the accepted value in C2:

=ABS(B2-C2)/ABS(C2)

Then format the cell as a percentage. Microsoft describes ABS as returning the absolute value of a number, and Google Sheets' help says it Returns the absolute value of a number. For the signed version use =(B2-C2)/ABS(C2). To compare a set of trials first, the standard deviation calculator shows how spread out they are, and the percentage increase calculator handles a change from an old value to a new one.

Questions and answers

What is the formula for percent error?

Percent error = |measured - accepted| / |accepted| x 100. For 2.45 against 2.70 that is 0.25 / 2.70 x 100 = 9.26%.

Can percent error be negative?

The usual percent error uses the absolute value, so it is 0 or more. The signed version is negative when the measured value is below the accepted value, such as -9.26% for 2.45 against 2.70.

Can percent error be more than 100%?

Yes. If the measured value is more than double the accepted value, or below zero when the accepted value is positive, the error is over 100%. Measuring 25 against an accepted 10 is a 150% error.

What if the accepted value is 0?

Percent error is undefined, because it would mean dividing by 0. Report the absolute error, the plain difference, instead.

What is a good percent error?

There is no single cut-off. It depends on the equipment and the experiment, so ask your teacher or check the lab manual. A smaller percent error means the result is closer to the accepted value.

How many significant figures should percent error have?

With the step by step rule, the difference keeps the last decimal place both values share, and the answer keeps the fewer figures of that difference and the accepted value. 2.45 against 2.70 gives 9.3%.

What is the difference between percent error and percent difference?

Percent error compares a result with an accepted value and divides by that value. Percent difference compares two results with each other and divides by their average.

Sources

Checked on 13 October 2026. If a rule has changed, please tell us.