49 g against a 50 g reference
|49 − 50| ÷ |50| × 100 = 2%
The signed difference is −1 g and the absolute error is 1 g. A 5% tolerance allows measurements from 47.5 g to 52.5 g, so 49 g is within the limit.
Measurements & comparisons
Percent Error Calculator
Compare a measured or calculated value with a reference, then check an optional percentage tolerance.
Calculate percent error
Percent error
Enter a measured value and reference, then select Calculate.
- Signed difference
measured − reference - Absolute error
- Relative absolute error
- Tolerance check
- Allowed measured values
Differences and interval bounds use the same unit as your inputs. Relative error is a ratio; percent error is that ratio × 100.
Calculation steps and exact values
≈ marks display rounding. Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.
Worked examples
30 against a reference of 10
|30 − 10| ÷ |10| × 100 = 200%
The absolute error is 20, twice the reference magnitude. Percent error has no 100% upper limit; a large discrepancy can produce a much larger percentage.
−18 against a reference of −20
|−18 − (−20)| ÷ |−20| × 100 = 10%
The signed difference is +2: the measured value is above the reference. The error percentage stays nonnegative because the denominator uses the reference magnitude.
Formula, tolerance, and rounding
Let m be the measured value and r the reference. The signed difference is m − r; the absolute error is |m − r|. For r ≠ 0, the relative absolute error is |m − r| ÷ |r|, and the percent error is 100 × |m − r| ÷ |r|.
For a tolerance t%, the allowed measured interval is r ± |r| × t ÷ 100. A measurement is within tolerance when its exact percent error is at most t; equality passes. Values above 100% are accepted for both percent error and the tolerance limit. A zero tolerance accepts only an exact match to a nonzero reference.
A zero reference makes the percentage and relative error undefined, including when both values are zero. The tool still gives the signed difference and absolute error, but it does not classify a percentage tolerance or show an allowed interval in this case.
The reference and measured value must use the same unit and scale. Ratios can change on scales whose zeros are shifted: Celsius and Fahrenheit temperature readings, for example, should not be used interchangeably for relative error. Choose a physically appropriate reference scale; this tool does not convert units or validate the scientific model.
Inputs accept at most 64 characters, 15 integer digits, and 10 decimal places, with a period as the decimal separator and optional thousands commas. Expressions, fractions, units, and scientific notation are not accepted. The optional tolerance must be nonnegative.
Arithmetic and tolerance comparisons retain exact fractions. Only displayed decimals are rounded, halfway away from zero, with trailing zeros omitted. ≈ marks a rounded value, including a nonzero result that displays as zero. Rounded interval boundaries do not change the exact pass/fail decision. Changing display precision does not add a recent-calculation entry.
This calculation compares the numbers you enter. It does not estimate measurement uncertainty, establish a confidence interval, or identify the cause of a discrepancy. A supplied reference can itself have uncertainty, and extra display digits do not improve a measurement.
References: University of Iowa — percent error formula and NIST — measurement error and uncertainty terminology.
Common questions
Is percent error the same as percent difference or percent change?
No. This tool compares one value against a designated reference and reports the magnitude of the relative discrepancy. Percent change usually preserves direction relative to an original value, while percent difference often compares two values without treating either as the reference. Their formulas and interpretations differ.
Why can a displayed 5% error be outside a 5% tolerance?
The display may round a slightly larger error to 5%. The tolerance check uses the exact, unrounded value. Increase the maximum decimal places or expand the exact calculation steps to inspect the distinction.
What happens when the reference is very close to zero?
A small nonzero reference can produce a very large percent error even for a small absolute difference. The calculator preserves that nonzero reference exactly. Consider the absolute error and whether a relative comparison makes sense for your measurement.
Does 0% error prove that a measurement is accurate?
An exact 0% means the entered values match a nonzero reference. It does not establish the quality of the reference, the measuring process, or the measurement uncertainty. A display of ≈ 0% instead means a small positive error was rounded.
Can I use a negative reference?
Yes. The percent error uses the magnitude of the reference, so it remains nonnegative. Whether a relative comparison is meaningful still depends on the quantity and scale. The signed difference is shown separately to preserve direction.