Enter the value you measured and the accepted value, and the page works out the percent error with every step. It also shows the signed error, so you can tell in your lab report whether your result came out high or low. In UK courses this is often called percentage error.
Enter the numbers
Everything is worked out in your browser. Nothing you type is sent anywhere.
Your answer
Your answer shows up here once you fill in both values.
What to enter
- Measured value
- The number you got in your experiment. It is also called the experimental value.
- Accepted value
- The number you compare it with: a textbook value, a data table value or the theoretical result. It is also called the true or theoretical value.
Worked examples
Measuring the acceleration of gravity
A class drops a ball and measures the acceleration as 9.5 m/s². The accepted value is 9.81 m/s². What is the percent error?
- Find the error: 9.5 – 9.81 = -0.31.
- Ignore the sign to get the absolute error: 0.31.
- Divide by the size of the accepted value: 0.31 ÷ 9.81 = 0.0316.
- Multiply by 100: 0.0316 × 100 = 3.160041%.
The percent error is 3.160041%. The signed error is -3.16%, which tells you the measurement came out below the accepted value.
A result that comes out high
A solution has an accepted concentration of 100 and you measure 102.
- Find the error: 102 – 100 = 2.
- Ignore the sign to get the absolute error: 2.
- Divide by the size of the accepted value: 2 ÷ 100 = 0.02.
- Multiply by 100: 0.02 × 100 = 2%.
The percent error is 2%, and the signed error is +2%, so the result is above the accepted value.
Percent error, percent difference and percent change
These three sound alike and use different bases. Percent error compares your result with a value that is known. Percentage difference compares two results with neither one known. Percentage change describes how a number moved from an old value to a new one.
| Question | Base | Answer |
|---|---|---|
| Percent error | The accepted value | 3.16% |
| Percentage difference | The average of both | 3.2108% |
| Percentage change | The old value | -3.16% |
The answers are close here because the numbers are close. They drift apart when the two values are far apart. Your lab manual will say which one to report.
What a good percent error looks like
There is no single cut-off. A good result depends on the equipment, the method and your course. A school balance can be off by a few percent, and a precision instrument can do far better. Use the number to start a discussion in your lab report: where could the error come from, and which way did it push your result?
How it is calculated
- Subtract the accepted value from your measured value to get the error.
- Ignore the sign to get the absolute error.
- Divide the absolute error by the accepted value.
- Multiply by 100 to turn it into a percent. The signed version keeps the plus or minus, so you know whether your result was high or low.
Percent error = |measured – accepted| ÷ |accepted| × 100
Signed error = (measured – accepted) ÷ |accepted| × 100
Assumptions to keep in mind
- The accepted value is the base. Dividing by your own measurement gives a different answer, and most lab manuals do not use it.
- Some courses report percent error with a sign, and some report only the size. The page shows both.
- If the accepted value is 0, the page asks you to use the plain difference, because you cannot divide by 0.
- The page does the arithmetic only. It does not judge whether your error is acceptable.
Mistakes that give the wrong answer
Dividing by the measured value
The error is measured against the accepted value. Dividing by what you measured changes the answer.
Mixing units
Both values must use the same unit. Convert one of them first if they differ.
Dropping the sign when your report needs it
If your course asks which way the error went, report the signed error as well as the size.
Reporting too many digits
Round to the precision your data supports. Two or three significant figures is common, but follow your course.
Questions students ask
How do I calculate percent error?
Subtract the accepted value from your measured value, ignore the sign, divide by the accepted value, then multiply by 100. For 9.5 against 9.81, that is 0.31 ÷ 9.81 × 100 = 3.16%.
Can percent error be negative?
The usual percent error is always positive, because it uses the absolute value. The signed error can be negative, which means your result was below the accepted value. The page shows both.
What is the difference between percent error and percentage error?
Nothing. Percent error is the US wording and percentage error is common in UK and Australian courses. The calculation is the same.
Is percent error the same as percent difference?
No. Percent error uses the accepted value as the base. Percent difference compares two numbers and uses their average. The table on this page shows both for the same pair.
What if I do not know the accepted value?
Then there is nothing to measure the error against. If you have two of your own results, use the percentage difference calculator.
