Calculators
Percent Error Calculator
Find percent error between measured and accepted values.
Percent error
|measured - accepted| / |accepted| x 100
Absolute error
0.2
Difference without direction
Signed error
-0.2
Positive means measured is higher; negative means lower.
Relative error
0.02
Percent error as a decimal ratio.
The accepted value must be nonzero. Results use the absolute accepted value in the denominator so negative reference values still produce a nonnegative percent error.
About This Tool
Percent error compares a measured or experimental value with an accepted, exact, or theoretical value. This calculator reports the usual nonnegative percent error along with absolute error, signed error, and relative error so you can see both the size of the difference and whether the measurement was above or below the reference. It is useful for science labs, measurement checks, estimation practice, and math homework where the accepted value is known.
How To Use It
- Enter the measured or experimental value from your observation, estimate, or calculation.
- Enter the accepted, theoretical, exact, or reference value. This value cannot be zero because it is the denominator.
- Read percent error for the magnitude of the mismatch, and use signed error when the direction of the difference matters.
Examples
Lab measurement
A measured value of 9.8 compared with an accepted value of 10 has an absolute error of 0.2 and a percent error of 2%.
Estimate above the reference
An estimate of 105 compared with an accepted value of 100 has a signed error of +5 and a percent error of 5%.
Negative reference value
For measured -48 and accepted -50, the signed error is +2 and the percent error is 4% because the denominator uses the absolute accepted value.
Useful Notes
Percent error formula
Percent error = |measured value - accepted value| / |accepted value| x 100. The absolute value makes the standard percent error nonnegative.
Signed error and direction
Signed error keeps direction: measured value - accepted value. A positive signed error means the measured value is higher than the accepted value; a negative signed error means it is lower.
Relative error
Relative error is the same comparison before multiplying by 100. For example, a relative error of 0.02 is a percent error of 2%.
Important limitation
Percent error is undefined when the accepted value is zero. In that case, compare absolute error or use another context-specific error measure instead of forcing a percentage.
FAQ
What is the difference between percent error and percent difference?
Percent error compares a measured value with a known accepted or reference value. Percent difference usually compares two observed values without treating either one as the accepted truth.
Can percent error be negative?
The standard percent error is not negative because it uses an absolute difference. The signed percent error shown by this calculator preserves direction when you need to know whether the measured value was high or low.
Why is the accepted value not allowed to be zero?
The formula divides by the accepted value. Division by zero is undefined, so a zero accepted value cannot produce a meaningful percent error.
Does this calculator round the result?
The display uses compact number formatting for readability, while the calculation is performed with JavaScript number precision in the browser.
Related Tools
Percentage Calculator
PopularFind percentages, percent change, increases, and decreases.
Statistics Calculator
Mean, median, mode, variance, standard deviation, and more.
Average Calculator
Calculate and compare four useful types of averages.
Scientific Calculator
Scientific math functions with degree and radian modes.