What Is Percentage Error and How to Calculate It
Percentage error is used to measure how far a calculated or measured value is from an expected or true value. It is commonly used in science, mathematics, engineering, and data analysis to evaluate accuracy.
Understanding percentage error helps you identify mistakes, improve precision, and compare results in a standardized way.
You can calculate percentage error instantly using our free percentage calculator.
What Is Percentage Error
Percentage error shows the size of the error relative to the correct value. It expresses the difference as a percentage, making it easier to compare errors across different measurements.
The smaller the percentage error, the more accurate the result.
Percentage Error Formula
Percentage error equals the absolute difference between the measured value and the true value, divided by the true value, multiplied by one hundred.
The absolute value is used so the error is always positive.
How to Calculate Percentage Error Step by Step
Step 1: Find the Difference
Subtract the true value from the measured value.
Step 2: Take the Absolute Value
Remove any negative sign so the result is positive.
Step 3: Divide by the True Value
This shows how large the error is relative to the correct value.
Step 4: Multiply by One Hundred
This converts the result into a percentage.
Percentage Error Example
If the true value is 50 and the measured value is 47, the difference is 3.
Dividing 3 by 50 gives 0.06. Multiplying by one hundred gives a percentage error of 6 percent.
A percentage error of 6 percent means the measurement is 6 percent away from the true value.
Why Percentage Error Matters
Percentage error helps you understand accuracy in a meaningful way. Instead of just knowing how much a value is off, you know how significant that error is.
This is especially important when comparing results across experiments, tests, or data sets.
Common Uses of Percentage Error
- Science experiments and lab results
- Engineering measurements
- Statistical analysis
- Forecasting and predictions
- Quality control checks
Percentage Error vs Percentage Change
Percentage error and percentage change are often confused, but they measure different things.
Percentage error compares a measured value to a true value. Percentage change compares an old value to a new value.
Knowing which one to use prevents incorrect conclusions.
Common Mistakes to Avoid
- Using the measured value as the denominator instead of the true value
- Forgetting to use the absolute value
- Confusing percentage error with percent difference
- Skipping multiplication by one hundred
Practice Problems
Try solving these examples, then verify your answers using the calculator.
- True value is 120, measured value is 114
- True value is 80, measured value is 86
- True value is 250, measured value is 240
Frequently Asked Questions
Can percentage error be greater than one hundred
Yes. If the measured value is far from the true value, the percentage error can exceed one hundred percent.
Is percentage error always positive
Yes. Because the absolute value is used, percentage error is always expressed as a positive number.
What does zero percentage error mean
A percentage error of zero means the measured value is exactly equal to the true value.
Conclusion
Percentage error is a simple but powerful way to measure accuracy. By comparing the difference between measured and true values relative to the true value, you can clearly understand how accurate a result is.
For fast and accurate calculations, use our free percentage calculator to compute percentage error instantly.