Percent Error Calculator

Percent error = |measured value − accepted value| ÷ |accepted value| × 100. Subtract the accepted (true) value from your measured value, drop the minus sign, divide by the accepted value and multiply by 100. For a measured 9.6 m/s² against the accepted 9.80665 m/s², that is 0.20665 ÷ 9.80665 × 100 = 2.11%.

First subtract: measured − accepted. Second, take the absolute value so the error is positive. Third, divide by the accepted value to get the relative error. Fourth, multiply by 100 and add a percent sign. For example a boiling point measured at 98.2 °C against 100 °C gives 1.8 ÷ 100 × 100 = 1.8%. The calculator shows these four steps with your numbers.

With the usual formula, no, because the absolute value removes the sign. Some teachers and textbooks use the signed version, (measured − accepted) ÷ accepted × 100, so a negative result means the measurement was too low and a positive one means it was too high. Tick Keep the sign to use that convention.

It depends on the experiment and equipment. In many school labs a result within about 5% is treated as reasonable and under 1% as very close, but precise instruments are expected to do far better, and rough estimates may accept 10% or more. Check what your course or method expects, and compare the error with the uncertainty of your instruments.

Absolute error is the plain size of the difference, |measured − accepted|, in the same units as the measurement — for example 0.2 m/s². Relative error divides that by the accepted value, giving a unitless fraction such as 0.0204. Percent error is simply the relative error multiplied by 100. Relative and percent error let you compare accuracy across different scales.

Percent error compares a measurement with a known correct value and divides by that correct value. Percent difference compares two values when neither is the reference, dividing their difference by their average: |a − b| ÷ ((|a| + |b|) ÷ 2) × 100. So 10 and 12 have a percent difference of 18.18%, whichever order you enter them.

Percent change measures how much a value grew or shrank over time, (new − old) ÷ |old| × 100, and keeps its sign: 50 to 75 is a 50% increase and 80 to 60 is a 25% decrease. Percent error measures how far a measurement is from the true value. They use a similar formula but answer different questions.

Percent error divides by the accepted value, and division by zero is undefined. If the true value is 0, for instance a reading that should be zero volts, report the absolute error instead, such as 0.03 V, or compare against the size of the instrument's range. The calculator shows a message rather than an infinite result.

Average the trials first, then calculate the percent error of that mean against the accepted value. You can also work out the percent error of each trial and average their sizes, the mean absolute percent error. The Multiple trials tab gives both, along with the standard deviation, which shows how consistent the trials were.

Some classes define accuracy that way, so a 2.11% error is 97.89% accurate, and the calculator shows this figure. Strictly, accuracy describes how close a result is to the true value and precision describes how close repeated results are to each other. A set of trials can be precise but inaccurate if every reading is off in the same direction.