What Is Percentage Error?
Percentage error expresses how far a measurement is from the true value as a percentage of the true value: percentage error = (measured − true) ÷ true × 100. A positive result means the measurement is above the true value and a negative result means it is below.
Many science courses report the absolute percentage error, which drops the sign. The calculator gives both, plus the symmetric percentage difference for cases where neither value is the "true" one. The true value must not be zero, because the formula divides by it.
Below you will find the formulas, a variables table, a worked example and answers to common questions such as percentage error versus percent difference.
How to Use the Percentage Error Calculator
- Enter the accepted (true) value.
- Enter your measured or estimated value.
- Use the absolute percentage error for a lab report unless your instructor wants the sign.
- Check the chart to see how your error compares with common 1%, 5% and 10% thresholds.
Percentage Error Formula
Percentage error
Absolute percentage error
Symmetric percentage difference
Percentage Error Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| Measured | Experimental or observed value | |
| True | Accepted or theoretical value | Cannot be zero |
| Error | Measured − True | Absolute error is its size |
| % error | Error ÷ True × 100 | Signed or absolute |
Percentage Error Worked Example
With the example values loaded in the calculator above, the steps are:
- Error = measured − true = 9.6 − 9.81 = -0.21.
- Relative error = error ÷ |true value| = -0.21 ÷ 9.81 = -0.0214067.
- Percentage error = relative error × 100 = -2.14067 %.
- Absolute percentage error = |-2.14067 %| = 2.14067 %.
Result: Percentage error = -2.14067 %; Absolute percentage error = 2.14067 %.
Worked Example: A Measured Value Against a True Value
The accepted value is 9.81 and the measured value is 9.6. The error is 9.6 − 9.81 = −0.21, and dividing by the true value gives −0.0214, a percentage error of −2.14%. The sign tells you the measurement was low. The absolute percentage error of 2.14% drops the sign and corresponds to an accuracy of 97.86%.
The percentage error is relative to the true value, so it is not symmetric between the two numbers. The symmetric percentage difference, 2.16% here, divides by the average of the two and is the better choice when neither value is the reference.
Percentage error, relative error and percentage difference
| Term | Base for the division | Use |
|---|---|---|
| Absolute error | None | Size of the miss in the original units |
| Relative error | True value | Miss as a fraction of the true value |
| Percentage error | True value | Relative error × 100 |
| Percentage difference | Average of the two values | Comparing two measurements when neither is “true” |
| Percentage change | Original value | Growth or decline over time |
What counts as a small percentage error?
It depends on the experiment. In a school physics lab, under 5% is often considered good; in precision analytical work, fractions of a percent are expected. The right threshold is set by the accuracy of your instruments and by any standards you must meet. The error should also be compared with the uncertainty in your own measurement: if your uncertainty is ±3%, a 2% error is within expected variation.
Should percentage error be positive or negative?
A signed result shows direction: positive when you measured too high, negative when too low. Many textbooks and lab manuals instead report the absolute value. If no instruction is given, the absolute percentage error is the safe choice; keep the sign in your notes if you are analysing systematic bias.
Where Percentage Error Is Used
Lab reports
Compare a measured value with an accepted value.
Signed and absolute error
See both the direction and the size of the error.
Accuracy
Read the accuracy as 100% minus the absolute error.
Symmetric difference
Compare two values when neither is the true one.
Common Percentage Error Mistakes to Avoid
- Divide by the true value, not by your measurement.
- Do not round the intermediate values; round only the final percentage.
- If the true value is 0 use absolute error instead.
- Use percent difference when comparing two experimental values with no accepted standard.
Percentage Error Terms and Definitions
- Accepted value
- The true or reference value from a standard, textbook or calibrated source.
- Systematic error
- An error that consistently pushes results in one direction.
Percentage Error FAQs
How do you calculate percentage error?
Subtract the true value from the measured value, divide by the true value and multiply by 100.
What is the difference between percent error and percent difference?
Percent error compares to a true value. Percent difference compares two values by dividing by their average, so neither is treated as the reference.
Can percentage error be negative?
Yes, if the measured value is below the true value. Many reports give the absolute value, which is never negative.
Can percentage error be more than 100%?
Yes, when the measured value is more than double the true value or has the opposite sign.
What is a good percent error?
Lower is better. Under 5% is often acceptable in teaching labs, and under 1% is considered excellent, but standards vary by field.
What if the true value is zero?
Percentage error is undefined because you cannot divide by zero. Report the absolute error instead.
What is the percentage error formula?
Percentage error = (approximate − exact) ÷ exact × 100. With exact 9.81 and measured 9.6 that gives −2.14%. The absolute percentage error drops the sign.
Is a negative percentage error bad?
The sign only shows direction. Negative means the measured value is below the true value. Use the absolute value when you only care about the size of the error.
What is the difference between percentage error and percentage difference?
Percentage error compares a measurement with a known true value. Percentage difference compares two values when neither is the reference, using their average as the base.
What if the exact value is zero?
The formula divides by the exact value, so it is undefined at zero. Report the absolute error instead.