Measurement error calculator
Percent Error Calculator: Find Percent Error
Compare an experimental or measured value with a known, accepted, or reference value in seconds. This percent error calculator shows the absolute error, relative error, signed direction, and the formula used so you can check a lab, classroom, quality-control, or measurement result.
Calculate percent error
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A measured value of 98 is 2 units below the accepted value of 100. The absolute error is 2, the relative error is 0.02, and the percent error is 2.00%.
The distance between measured and accepted values.
Absolute error divided by the accepted value's magnitude.
The observation or experimental result you entered.
The reference value used as the comparison base.
Percent error formula
|98 - 100| / |100| x 100 = 2 / 100 x 100 = 2.00%How this result was calculated
- Subtract the accepted value from the measured value: 98 - 100 = -2.
- Take the absolute difference: |-2| = 2 units of error.
- Divide by the magnitude of the accepted value: 2 / |100| = 0.02.
- Multiply by 100 to express the relative error as a percentage: 0.02 x 100 = 2.00%.
Percent error calculator examples
Choose a familiar measurement, then replace the example values with your own result and reference.
Laboratory mass
A scale reads 9.8 g while the accepted mass is 10 g. The absolute error is 0.2 g and percent error is 2%.
Temperature reading
A sensor reports 21.4 C against a 20 C reference. The result is 7% error and the signed reading is high.
Close measurement
A measured length is 49.95 mm against a 50 mm standard. The small difference is easier to read as a percentage.
How to use this percent error calculator
Keep the comparison transparent: enter two values in the same units and review the direction before reporting the percentage.
Enter the measurement
Type the experimental, observed, or calculated result in the measured value field. Decimals and negative numbers are accepted when they make sense for the measurement.
Enter the reference
Use the accepted, theoretical, target, or certified value as the denominator. It must not be zero because percent error is relative to its magnitude.
Calculate
Select Calculate percent error. The result panel shows the absolute difference, relative error, percentage, and whether the measured value is high, low, or equal.
Report with context
Include units, the reference value, rounding, and the reason the reference is trusted. A percentage alone cannot explain calibration quality or data collection conditions.
What is percent error?
Percent error describes how far a measured value is from an accepted or reference value relative to the reference. The absolute difference is divided by the absolute accepted value and multiplied by 100. Using the denominator's magnitude keeps the reported size non-negative even when a signed quantity is negative.
In a classroom laboratory, the accepted value may come from a theory, a published constant, or a calibrated standard. In quality control it may be a specification or certified measurement. The calculator does the arithmetic; you still need to decide whether the chosen reference, units, instrument resolution, and rounding are appropriate.
The percentage is a size-of-error measure. The signed difference supplies direction: a positive measured-minus-accepted value is high, while a negative value is low. This page reports both so a 2% result does not hide which way the reading moved.
Percent error is different from percent difference. Percent difference compares two experimental values when neither is automatically the accepted base, while percent error compares one result with a designated reference. Use the wording required by your assignment, report, or quality procedure.
A low percentage is not proof of a perfect measurement
A small percent error can still be meaningful when the tolerance is tight. Consider uncertainty, significant figures, repeatability, and the measurement method before deciding whether the result is acceptable.
Percent error formulas explained
The calculator keeps each step visible so you can reproduce the result in a lab notebook, spreadsheet, or report.
Absolute error
absolute error = measured value - accepted valueThe signed difference shows direction. Its absolute value is the distance between the two values and keeps the size independent of high or low direction.
Relative error
relative error = |measured - accepted| / |accepted|Relative error expresses the absolute difference as a fraction of the reference magnitude. It has no unit and is usually smaller than the percent form by a factor of 100.
Percent error
percent error = |measured - accepted| / |accepted| x 100Multiply relative error by 100 and add the percent sign. Choose sensible rounding; extra digits do not create extra measurement accuracy.
Signed direction
direction = measured value - accepted valueA positive difference means the measurement is high, a negative difference means it is low, and zero means it matches the reference exactly.
How to read a percent error result
Start with the reference and the units. A 0.5 gram difference means something different for a 1 gram sample than for a 1 kilogram sample. The percent error puts the difference on a relative scale, but it does not replace an uncertainty budget or a stated tolerance.
Use absolute error when the allowed difference is expressed in the original unit, such as plus or minus 0.2 mm. Use percent error when the requirement scales with the reference or when you need to compare measurements made at different magnitudes. Keep the signed direction in your notes when a bias matters.
Rounding should match the precision of the inputs and the reporting rule. If the accepted value is written as 20 C, reporting 7.000000% may suggest more certainty than the source supports. The precision selector changes the display only; it does not change the underlying arithmetic.
| Result | Meaning | Useful when |
|---|---|---|
| Absolute error | The signed difference, or its magnitude, between the measured and accepted values. | A tolerance is stated in the original unit. |
| Relative error | Absolute error divided by the magnitude of the accepted value. | You want a unit-free fraction before converting to percent. |
| Percent error | Relative error multiplied by 100. | You need a compact comparison across measurements or a report format. |
| Direction | Whether the measured value is above, below, or equal to the reference. | A systematic high or low reading matters. |
Percent error limits and edge cases
These checks keep the result meaningful and prevent a valid-looking percentage from hiding a bad input.
Accepted value of zero
The calculator rejects zero as the reference because division by zero has no defined result. Use an absolute difference or a different reference rule when zero is the meaningful baseline.
Matching values
When measured and accepted values are identical, absolute error, relative error, and percent error are all zero. The direction is reported as a match.
Negative quantities
Signed values are accepted. The denominator uses its magnitude for the percentage, while the signed difference still identifies whether the measurement is high or low.
Very small references
A small nonzero reference can make a modest absolute difference produce a large percentage. Check the scale and precision before treating that percentage as surprising.
Different units
Do not compare centimeters with meters, grams with kilograms, or Celsius with Fahrenheit without converting first. Both fields must describe the same quantity in the same unit.
Rounding and significant figures
The tool rounds only the displayed cards. Report no more precision than your instrument, accepted value, and assignment or quality standard support.
More than one observation
For repeated readings, calculate each error or summarize the mean and uncertainty using a documented method. One percent error cannot describe repeatability by itself.
Percent error calculator FAQ
Common questions about the percent error formula, reference values, and reporting.
Ready to check a measurement?
Enter the measured and accepted values, confirm the units match, and use the formula line to verify the percent error before you report it.