Calculators
Percent Error Calculator
Find percent error, compare measurements, or solve for a measured value.
Percent Error Calculator tool
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About This Tool
Percent error compares a measured or experimental value with an accepted, exact, or theoretical value. When neither value is an accepted reference, percent difference compares two measurements using their average magnitude instead. This calculator supports both cases and shows the substituted steps, absolute difference, and relative result. It is useful for science labs, measurement checks, estimation practice, and math homework.
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.
- Choose Two measurements instead when neither value is the accepted reference; the result will use the percent difference formula.
- Choose Solve measured value when you know the accepted value, percent error, and whether the measurement was above or below the reference.
- Optionally add the shared unit used by both values so absolute and signed errors are labeled correctly.
- Round by decimal places or significant figures for a worksheet or lab report. This changes the presentation without changing the underlying calculation.
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.
Zero measured value
A measured value of 0 compared with an accepted value of 20 has an absolute error of 20 and a percent error of 100%. A zero measured value is valid as long as the accepted value is not zero.
Two experimental measurements
Measurements of 9.8 and 10 have an absolute difference of 0.2 and a percent difference of about 2.02%, using their average magnitude of 9.9 as the denominator.
Recover a measured value
An accepted value of 100 with a 5% error corresponds to a measured value of 105 when the measurement is above the reference, or 95 when it is below.
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%.
Accepted value must be the reference
Use the accepted, exact, theoretical, or reference value as the denominator for percent error. If neither value is the reference, switch to Two measurements and calculate percent difference instead.
Percent difference formula
Percent difference = |first value - second value| / ((|first value| + |second value|) / 2) x 100. It treats the measurements symmetrically, so changing their order does not change the result.
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.
Single comparison, not uncertainty analysis
This calculator compares one measured value with one accepted value. It does not calculate standard deviation, confidence intervals, calibration uncertainty, or repeated-trial error statistics.
Rounding the reported result
Choose decimal places for a fixed number of digits after the decimal point, or significant figures for lab-report notation that counts meaningful digits from the first nonzero digit. The control rounds shown and copied values only; it does not round intermediate calculations.
Solve for the measured value
Convert the percent error to an absolute error with (percent error / 100) x |accepted value|. Add that error for a measurement above the reference or subtract it for one below. Because the usual percent error formula discards the sign, the direction must be known separately.
Use the same unit for both values
Percent error and relative error are unitless, but measured and accepted values must use compatible units. Add an optional unit such as g, cm, or °C to label absolute and signed errors in the results and copied summary.
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 compares two observed values without treating either one as the accepted truth. Choose the matching mode above to calculate either result.
Can percent error be negative?
The standard percent error is not negative because it uses an absolute difference. Use signed error to see whether the measured value was above or below the accepted value.
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.
Can the measured value be zero?
Yes. A measured value of zero is valid when the accepted value is nonzero; the percent error is then based on how far zero is from the accepted reference.
Does this calculator round the result?
Yes. Choose decimal places or significant figures for displayed and copied values. The underlying calculation still uses full JavaScript number precision in your browser.
How do I find the measured value from percent error?
Multiply the nonnegative percent error by the absolute accepted value and divide by 100 to get the absolute error. Then add it for a measurement above the accepted value or subtract it for one below. Use Solve measured value above to do both steps.