Percent Error CalculatorFree online math calculator — instant results, no sign-up
Error between an observed and true value.
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About the Percent Error Calculator
The Percent Error Calculator determines the relative difference between an experimentally measured or observed quantity and a known true or theoretical value. It is commonly used by science students, researchers, and engineers to evaluate the accuracy of experimental measurements and instruments.
- Observed value
- The measured, estimated, or experimental measurement obtained, expressed in any real unit.
- True value
- The accepted, theoretical, or standard reference value; must be in the same unit as the observed value and cannot equal zero.
Formula and method
Percent error = (|Observed value − True value| / |True value|) × 100
- Observed valueThe experimentally measured or estimated value
- True valueThe standard, theoretical, or accepted reference value
The calculator takes the absolute difference between the observed value and the true value, divides that result by the absolute value of the true value, and multiplies by 100 to yield a percentage. The final result is rounded to three decimal places.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Observed value9.6
- True value9.81
Results
- Percent error2.141%
How to use the Percent Error Calculator
- 1Subtract the true value from the observed value.
- 2Take the absolute value of the difference to find the absolute error.
- 3Divide the absolute error by the absolute value of the true value.
- 4Multiply by 100 and round the resulting percentage to three decimal places.
Reading your result
A percent error of 0% indicates that the measurement perfectly matched the theoretical value. Lower percentages reflect higher accuracy, whereas higher percentages indicate greater deviation from the accepted standard.
Limitations
This calculation does not indicate the direction of error (whether the observation was an overestimate or underestimate) because it takes the absolute value. It also cannot be calculated if the true value is zero, as division by zero is undefined.
Common questions
Can percent error be negative?+
In this calculator, percent error is always non-negative because the absolute value of the difference is used. Some disciplines omit the absolute value to preserve sign, but standard convention uses absolute value to measure overall deviation.
What happens if the true value is zero?+
If the true value is zero, percent error cannot be computed because division by zero is mathematically undefined. In such cases, absolute error rather than relative error must be reported.
What is the difference between percent error and percent difference?+
Percent error compares an experimental measurement to an established, known true value. Percent difference compares two experimental measurements of equal standing by dividing their difference by their average.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.