Case 1
- Measured value
- 9.8
- True (accepted) value
- 9.80665
0.067811%
Open with these valuesPercent Error Calculator
0.067811%
Result: 0.067811 %Percent error measures a single reading against a value that is already known to be right. It is the gap between the two, without its sign, as a percentage of the true value — so it never comes out negative. If neither value is the reference, you want percentage difference instead.
The numbers at a glance
Held fixed: Measured value 9.800000.
| True (accepted) value | Result (%) |
|---|---|
| 2.500000 | 292.000000 |
| 5.000000 | 96.000000 |
| 7.500000 | 30.666667 |
| 9.806650Your value | 0.067811 |
| 10.000000 | 2.000000 |
| 12.500000 | 21.600000 |
| 15.000000 | 34.666667 |
| 17.500000 | 44.000000 |
Worked examples
Case 2
- Measured value
- 8
- True (accepted) value
- 10
20.000000%
Open with these valuesCase 3
- Measured value
- 12
- True (accepted) value
- 10
20.000000%
Open with these valuesHow it's calculated
percent error = |measured − true| ÷ |true| × 100
- StepSubtract the true value from the measured value and drop the minus sign.
- StepDivide that gap by the true value, again without its sign.
- ResultMultiply by 100 to read the error as a percentage.
What this number means
The denominator is the true value
The gap is divided by the accepted value, not by the measurement and not by the average of the two. That reference point is what separates percent error from percentage difference.
The result is never negative
Both the gap and the true value are taken as absolute values, so the figure states the size of the error and not its direction. Measuring 8 against a true 10 and measuring 12 against a true 10 both give 20 %.
A true value of zero has no percent error
The formula divides by the true value, so the page stays empty when it is 0. The measured value itself may be zero or negative: 0 against a true 10 is 100 %.
The formula stands verbatim in the source
Math is Fun gives it as |Approximate − Exact| ÷ |Exact| × 100 %, with worked examples such as |70 − 80| ÷ 80 = 12.5 %. Checked on 2026-08-25.
Commonly misread
A minus sign in front of the error shows the reading was low.
The absolute value removes the direction, so the result never comes out negative. Reading 8 or reading 12 against a true 10 both give 20 %.
The measured value goes in the denominator.
The true value does. That is why there is no result when the true value is zero, while a measured zero is perfectly fine.
A negative scale needs a different rule.
It uses the same one: −5 against a true −4 gives 25 %, because numerator and denominator are both taken as absolute values.
Anything under 5 % is a good percent error.
That is the usual target in a school physics lab. Precision metrology allows only a small fraction of a percent, so compare against the tolerance of your own task.
Reference table
| Measured, true | Reading | Percent error |
|---|---|---|
| 10, 10 | Exact hit | 0.000000 |
| 9.8, 9.80665 | Gravity against the standard value | 0.067811 |
| 8, 10 | Measured too low | 20.000000 |
| 12, 10 | Measured too high, same size of error | 20.000000 |
| -5, -4 | Negative scale, same rule | 25.000000 |
| 0, 10 | Nothing registered at all | 100.000000 |
Questions
How do I calculate percent error?
Subtract the true value from the measured value, take the absolute value, divide by the absolute true value and multiply by 100. Measuring 9.8 against a true 9.80665 gives |9.8 − 9.80665| ÷ 9.80665 × 100 ≈ 0.068 %.
Why is percent error never negative?
The formula uses the absolute value of the difference, so it measures the size of the error and not its direction. Measuring 8 against a true 10 and measuring 12 against a true 10 both give 20 %.
What if the true value is zero?
Percent error is undefined then, because the formula divides by the true value. The calculator shows no result in that case. The measured value itself may be negative or zero without any problem.
How is percent error different from percentage difference?
Percent error compares a measurement against a known accepted value, so it has a clear reference. Percentage difference compares two values of equal standing and divides by their average instead. Use percent error in a lab where the accepted value is known.
What counts as a good percent error?
Lower is more accurate, and a value near 0 % means the reading sits very close to the true value. A school physics lab often aims for under 5 %, while precision metrology allows only a small fraction of a percent. Always compare against the tolerance of your own task.
Sources and last check
Information, not professional advice.