To calculate percentage error, subtract the accepted value from the experimental value, use the absolute value of the difference, divide it by the accepted value, and multiply by 100. For example, if a measured value is 48 and the accepted value is 50, the absolute error is 2. Dividing 2 by 50 and multiplying by 100 gives a percentage error of 4%.
Use the Percentage Calculator on the homepage to divide the absolute error by the accepted value and verify the percentage result.
A measured value of 48 differs from an accepted value of 50 by 2, producing a percentage error of 4%.
What Percentage Error Means
Percentage error describes the size of an error relative to an accepted, theoretical, expected, or known value. It converts the difference into a percentage so that errors involving different-sized values can be compared.
An absolute error of 2 may be small when the accepted value is 1,000 but large when the accepted value is 5. Percentage error provides the missing context.
This calculation is commonly used in experiments, laboratory work, measurement analysis, forecasting, engineering, quality control, and comparisons between estimated and known results.
Percentage Error Formula
Subtract the accepted value from the experimental or measured value. Use the absolute value of this difference so that the reported percentage error is normally non-negative.
Divide the absolute error by the accepted value. The accepted value is the reference against which the measurement is judged.
Multiply by 100 to convert the decimal ratio into a percentage.
Worked Example: Measured Value 48, Accepted Value 50
Subtract the accepted value from the measured value: 48 − 50 = −2.
Use the absolute value, which makes the error 2. Divide 2 by 50 to get 0.04.
Multiply by 100. The percentage error is 4%.
Step 1: Identify the Experimental Value
The experimental value is the result obtained through measurement, observation, estimation, testing, or calculation.
It may also be called the measured value, observed value, estimated result, actual reading, or calculated outcome, depending on the context.
Make sure this value is expressed in the same unit as the accepted value before comparing them.
Step 2: Identify the Accepted Value
The accepted value is the trusted reference used to assess the experimental result.
It may come from a published standard, theoretical calculation, calibrated instrument, verified dataset, manufacturer specification, or confirmed result.
Percentage error is only meaningful when the accepted value is appropriate and reliable for the comparison.
Step 3: Find the Absolute Error
Subtract the accepted value from the experimental value. The result may be positive or negative depending on whether the measurement is above or below the reference.
Use the absolute value when the objective is to report the magnitude of the error.
For a measured value of 102 and accepted value of 100, the absolute error is 2. For a measured value of 98, it is also 2.
Step 4: Divide by the Accepted Value
Divide the absolute error by the accepted value rather than the experimental value.
This calculates the error as a proportion of the trusted reference amount.
Using the experimental value as the denominator produces a different percentage and does not follow the standard percentage-error formula.
Step 5: Multiply by 100
Multiply the error ratio by 100 to convert it to percentage form.
A ratio of 0.04 becomes 4%, while a ratio of 0.0075 becomes 0.75%.
Round only after completing the full calculation so that early rounding does not distort the result.
How to Calculate Percentage Error on a Calculator
Enter the measured value minus the accepted value, apply the absolute value, divide by the accepted value, and multiply by 100.
For a measurement of 74 and accepted value of 80, calculate |74 − 80| ÷ 80 × 100. The result is 7.5%.
The Percentage Calculator can calculate the percentage represented by the absolute error relative to the accepted value.
Measurement Example
Suppose a measured length is 19.6 centimetres while the accepted length is 20 centimetres.
The absolute error is 0.4 centimetres. Divide 0.4 by 20 to get 0.02.
The percentage error is 2%.
Forecasting Example
Suppose a forecast predicts 1,150 sales, while the confirmed result is 1,000 sales.
The absolute error is 150. Divide 150 by the accepted result of 1,000 and multiply by 100.
The forecast has a percentage error of 15%.
Percentage Error vs Absolute Error
Absolute error is the numerical difference between the experimental and accepted values.
Percentage error expresses that difference relative to the accepted value.
An absolute error of 10 has a percentage error of 10% when the accepted value is 100, but only 1% when the accepted value is 1,000.
Percentage Error vs Percentage Difference
Percentage error requires an accepted or reference value. Percentage difference is used when both values are treated equally.
Percentage error divides by the accepted value, while percentage difference divides by the average of the two values.
Use the formula that matches the relationship between the numbers rather than choosing based only on the wording.
Can Percentage Error Exceed 100%?
Yes. Percentage error can exceed 100% when the absolute error is greater than the accepted value.
If the accepted value is 20 and the measured value is 50, the error is 30. Dividing 30 by 20 and multiplying by 100 gives 150%.
A result above 100% indicates that the measurement differs from the reference by more than the entire accepted amount.
What Happens When the Accepted Value Is Zero
The standard percentage-error formula cannot be used when the accepted value is zero because division by zero is undefined.
The numerical error can still be reported, but no standard finite percentage error exists.
Another scale, tolerance, absolute difference, or domain-specific method may be more appropriate in that situation.
Signed Error vs Absolute Percentage Error
Some analyses retain the sign of the error to show whether the result is above or below the accepted value.
A positive signed error may indicate overestimation, while a negative error may indicate underestimation.
When the question asks simply for percentage error, the absolute value is normally used unless the instructions specify signed percentage error.
Common Mistakes
A common mistake is dividing by the experimental value instead of the accepted value.
Another is leaving a negative sign in a calculation that asks for absolute percentage error.
Using values with different units, rounding too early, or confusing percentage error with percentage difference can also lead to incorrect results.
Conclusion
To calculate percentage error, find the absolute difference between the experimental and accepted values, divide by the accepted value, and multiply by 100.
Use the accepted value as the reference and confirm whether the task requires absolute or signed error.
Use the Percentage Calculator on Percentage.click to verify the percentage represented by your error value.
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FAQs
What is the formula for percentage error?
Subtract the accepted value from the experimental value, use the absolute difference, divide by the accepted value, and multiply by 100.
What is the percentage error when the measured value is 48 and the accepted value is 50?
The absolute error is 2. Dividing 2 by 50 and multiplying by 100 gives a percentage error of 4%.
Why is the accepted value used as the denominator?
The accepted value is the reference against which the experimental result is evaluated.
Can percentage error be greater than 100%?
Yes. It exceeds 100% when the absolute error is larger than the accepted value.
Is percentage error the same as percentage difference?
No. Percentage error uses an accepted value, while percentage difference treats both values equally and divides by their average.