Percentage error measures how far an estimated, measured, or expected value is from the actual value. It is commonly used in maths, science, measurements, forecasts, finance, and everyday comparisons where you want to know how large an error is relative to the true value.
Use the calculator to check the number quickly, then read the guide for formulas, examples, and common mistakes.
What Is Percentage Error?
Percentage error shows the size of an error as a percentage of the actual value.
For example, if the actual value is 100 and your estimate is 90, the difference is 10. Compared with the actual value of 100, the percentage error is 10%.
This makes the error easier to understand than only looking at the raw difference.
Percentage Error Formula
The percentage error formula is: percentage error = absolute error divided by actual value multiplied by 100.
Absolute error means the positive difference between the estimated value and the actual value.
In formula form, it is often written as: percentage error = |estimated value - actual value| ÷ actual value × 100.
Why Absolute Error Is Used
Absolute error ignores whether the estimate was too high or too low.
If the actual value is 100 and the estimate is 90, the difference is -10, but the absolute error is 10.
If the estimate is 110, the difference is 10. In both cases, the size of the error is 10.
Step 1: Find the Actual Value
The actual value is the correct, known, accepted, or real value.
This is the value used as the base of the percentage error calculation.
For example, if the real weight is 50 kg, then 50 is the actual value.
Step 2: Find the Estimated or Measured Value
The estimated value is the value you predicted, measured, calculated, or observed.
This value is compared with the actual value.
If your measurement says 48 kg when the actual weight is 50 kg, then 48 is the measured value.
Step 3: Find the Difference
Subtract the actual value from the estimated value.
Using the example, 48 - 50 = -2.
The negative sign shows the estimate was lower than the actual value, but percentage error usually uses the size of the error.
Step 4: Use the Absolute Difference
The absolute difference turns the error into a positive value.
In the example, the absolute difference is 2.
This means the measurement was off by 2 units.
Step 5: Divide by the Actual Value
Now divide the absolute difference by the actual value.
Using the example, 2 ÷ 50 = 0.04.
This shows the error as a decimal compared with the actual value.
Step 6: Multiply by 100
Multiply the decimal by 100 to convert it into a percentage.
0.04 × 100 = 4%.
So the percentage error is 4%.
Example: Percent Error in Measurement
Suppose the actual length is 200 cm and the measured length is 190 cm.
The absolute error is |190 - 200|, which equals 10.
Percentage error is 10 ÷ 200 × 100, which equals 5%.
Example: Forecast Error
Suppose a forecast expected 1,000 visits, but the actual visits were 1,250.
The absolute error is |1,000 - 1,250|, which equals 250.
Percentage error is 250 ÷ 1,250 × 100, which equals 20%.
Percentage Error vs Percentage Change
Percentage error compares an estimate with an actual value.
Percentage change compares an old value with a new value.
For before-and-after comparisons, read Percentage Change Formula.
Percentage Error vs Percentage Points
Percentage error is not the same as percentage points.
Percentage points are used when comparing two percentage values directly, such as 10% and 15%.
For that difference, read Percentage Points vs Percent.
Common Mistakes to Avoid
The first mistake is dividing by the estimated value instead of the actual value.
The second mistake is forgetting to use the absolute difference when only the size of the error matters.
The third mistake is using percentage error for a situation that is really percentage change.
Use the Calculator
Use the Percentage Calculator for general percentage calculations.
If your site has a specific percentage error calculator, you can also use it for direct percent error questions.
For the main percentage guide, read How to Calculate Percentage.
Conclusion
Percentage error shows how large an error is compared with the actual value.
Use the absolute difference between estimated and actual values, divide by the actual value, and multiply by 100.
Related guides and tools
FAQs
What is the percentage error formula?
Percentage error = absolute error divided by actual value, multiplied by 100.
What is absolute error?
Absolute error is the positive difference between the estimated value and the actual value.
Should percent error use actual value or estimated value?
Percent error usually uses the actual value as the base.
Is percentage error the same as percentage change?
No. Percentage error compares an estimate with an actual value, while percentage change compares an old value with a new value.