How to use the percent error calculator
- Enter your measured (experimental) value.
- Enter the accepted (true) value, which cannot be zero.
- Open the advanced options to change the number of decimal places.
- Read the percent error, the signed error that shows the direction, the absolute error and the relative error.
Formula
error = measured - accepted
percent error = |error| / |accepted| x 100
relative error = |error| / |accepted|
The signed percent error keeps the minus sign when the measurement is below the accepted value. The page uses the size of the accepted value, so negative accepted values work.
Measuring gravity
A student measures the acceleration of gravity as 9.4 and the accepted value is 9.81. The error is 9.4 - 9.81 = -0.41. The percent error is 0.41 / 9.81 x 100 = 4.18%, the signed version is -4.18%, and the relative error is 0.0418.
The measurement is 95.82% of the accepted value. If the measured value were -9 and the accepted value -10, the percent error would be 1 / 10 x 100 = 10%, and a measurement that matches exactly has 0% error.
Percent error and percent change
Percent error compares a measurement with a value you trust, so the accepted value is the base of the fraction. Percent change compares an old value with a new one, so the old value is the base. The two formulas look similar but answer different questions. Use the percent change calculator when neither value is a standard to be matched.
Reading the result
A small percent error means the measurement is close to the accepted value, but how small is good enough depends on the instrument and the experiment. Percent error does not show the uncertainty of a measurement. For that, repeat the measurement and look at the spread with the standard error calculator, and for simple percentages use the percentage calculator.
Assumptions and limits
- The accepted value is treated as exact. If it has its own uncertainty, percent error does not show it.
- The accepted value cannot be zero, because the formula divides by it.
- Units are not checked. Both values must use the same unit.
- Decimal places only affect how the results are shown. The calculation uses full precision.
Frequently asked questions
What is the percent error formula?
Subtract the accepted value from the measured value, take the absolute value, divide by the absolute accepted value and multiply by 100. For 9.4 against 9.81 that is 0.41 / 9.81 x 100 = 4.18%.
Can percent error be negative?
The usual percent error is a size, so it is not negative. The signed version keeps the sign to show whether you measured too low or too high, and the page shows both.
Why can the accepted value not be zero?
The formula divides by the accepted value, and dividing by zero has no answer. If the true value is zero, report the absolute error instead.
How is percent error different from percent difference?
Percent error compares one measurement with a value taken as true. Percent difference compares two measurements when neither is known to be right, and uses their average as the base.