Percent Error Calculator

How to use the percent error calculator

1. Enter your measured value, the result from your experiment or estimate. To use several trials, type them separated by commas; the calculator uses their mean.
2. Enter the accepted value, the reference you are comparing with: a textbook constant, a manufacturer’s specification, or a known standard.
3. Read the percent error and the signed error underneath. The absolute error, in your own units, is also shown.

Keep the units the same for both numbers. Comparing a density in g/cm³ with one in kg/m³ would give a meaningless percentage.

The percent error formula

The open chemistry textbook on LibreTexts (Introductory Chemistry, section 3.13) works an example with aluminum. Its accepted density is 2.70 g/cm³. A student measures 2.45 g/cm³. The error is 2.45 − 2.70 = −0.25 g/cm³, and the percent error is 0.25 ÷ 2.70 × 100 = 9.26%. The calculator opens on those numbers.

Two more checks. A pendulum lab that finds gravity to be 9.6 m/s² against an accepted 9.81 m/s² has a percent error of 0.21 ÷ 9.81 = 2.14%. An estimate of the speed of light of 2.2 × 10⁸ m/s against 2.998 × 10⁸ m/s is off by 26.6%; the University of Iowa’s physics glossary uses that example.

The divisor is the accepted value, not your measurement. That keeps the comparison anchored to the reference, so two students with different results are measured against the same yardstick.

Absolute or signed percent error?

Most lab manuals report the absolute value, which is zero or positive, so a 9.26% error reads the same whether the result was high or low. LibreTexts notes that the error is negative when the experimental value is below the accepted value and that the absolute value is used to avoid confusion.

The sign is still worth recording. If every trial comes out low, that points to a systematic error, such as a scale that isn’t zeroed or heat lost to the surroundings, rather than random scatter. The signed error line shows “measured is high” or “measured is low” for that reason. If your instructor asks for signed percent error, report that figure with its sign.

Percent error versus percent difference

Percent error needs a reference value you trust. When you only have two of your own results, such as two methods of measuring the same speed, neither is “correct,” and the right comparison is percent difference. Clemson University’s physics lab tutorial makes exactly that distinction.

It divides by the average of the two values, so swapping them doesn’t change the answer. The calculator shows it alongside percent error. For the aluminum example, the percent difference between 2.45 and 2.70 is 9.71%, a little larger than the percent error because the average, 2.575, is smaller than 2.70.

Accuracy, precision and several trials

Percent error measures accuracy: how close a result is to the true value. It says nothing about precision, which is how close repeated measurements are to each other. Texas A&M’s physics lab manual points out that an experiment can be very precise and still inaccurate, for instance when equipment hasn’t been calibrated.

With several trials, enter them all. The calculator averages them and finds the percent error of the mean. Three trials of 9.7, 9.9 and 9.8 m/s² average 9.8, which is 0.10% from 9.81. To describe precision as well, put the same trials into the standard deviation calculator; a small standard deviation with a small percent error means your result is both precise and accurate.

What counts as a good percent error?

There is no single cutoff. The Texas A&M manual notes that an error of 5% or 10% might be acceptable in some experiments and a sign of a poorly run one in others; it depends on the method and the instruments. A simple pendulum timed with a phone stopwatch may land within a few percent of 9.81 m/s². A calibrated balance should agree with a reference mass far more closely than that.

A more useful question is whether the percent error is larger than your measurement uncertainty. If your instruments can only resolve to about 2%, a 1.5% error is consistent with a careful measurement, while a 9% error suggests something else went wrong.

When percent error breaks down

• An accepted value of zero. You can’t divide by zero, so percent error is undefined. Report the absolute error in units instead.
• Accepted values near zero. A tiny reference makes small absolute errors look huge. A temperature of 0.5 °C measured as 1.0 °C is a 100% error, but only half a degree off.
• Negative accepted values. The calculator divides by the size of the accepted value, so −11 against −10 is a 10% error, as you would expect.
• Rounding. Round the percent error to a sensible number of significant figures, usually two or three, since it can’t be more precise than your measurement.

A worked lab example

Suppose you find the density of an aluminum block. It has a mass of 50.0 g, and water displacement gives a volume of 19.5 cm³. The density is 50.0 ÷ 19.5 = 2.564 g/cm³. Against the accepted 2.70 g/cm³, the error is −0.136 g/cm³ and the percent error is 0.136 ÷ 2.70 × 100 = 5.0%, with the result on the low side.

A low density means either the mass was read low or the volume high. Reading the meniscus at the wrong height, or air bubbles clinging to the block, would both add apparent volume. That is the kind of reasoning a lab report’s error discussion is looking for, and the signed error points you in the right direction.

Percent error outside the lab

The same formula measures how good an estimate or forecast was, with the actual result playing the part of the accepted value. A project budgeted at $12,000 that cost $13,500 has a percent error of 1,500 ÷ 13,500 = 11.1%, with the estimate on the low side. Tracking this figure across jobs shows whether your estimates tend to run high or low.

Relative error is the same ratio without the × 100: 0.0926 instead of 9.26%. Very small errors are often written in parts per million, where 1 ppm is 0.0001%.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• Percent error = |measured − accepted| ÷ |accepted| × 100; the signed version keeps the direction.
• With several trials, the measured value is their mean.
• The accepted value can’t be 0; values are compared in the units you enter.
• Percent difference = |a − b| ÷ average of a and b × 100, for comparing two results without a reference.

Sources

1. Chemistry LibreTexts, 3.13: Percent Error (Introductory Chemistry). Percent error = |experimental − accepted| ÷ accepted × 100%, with aluminum density measured at 2.45 g/cm³ against an accepted 2.70 g/cm³ giving 9.26%.
2. Clemson University, Department of Physics and Astronomy, Physics Tutorial: % Error & % Difference. Percent error compares a measurement with an accepted value; percent difference compares two measurements when there is no accepted value.
3. Texas A&M University, Visual Physics Laboratory, Error Theory (lab manual). Standard deviation describes precision, percent error describes accuracy, and whether a 5% or 10% error is acceptable depends on the method and instruments.
4. University of Iowa, Imaging the Universe (Physics and Astronomy), Percent Error Formula. Worked example comparing an early estimate of the speed of light, 220,000 km/s, with the accepted 299,800 km/s.

Last reviewed November 2, 2026. Report percent error to two or three significant figures, consistent with your measurements.