Percentage Error Calculator
Calculate percentage, absolute, and relative error
Percentage Error Calculator tool
Results
Percentage Error
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Absolute Error
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Relative Error
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Formula:
|95 - 100| / 100 × 100 = 0%
Step-by-step:
- 1.Calculate difference: 95 - 100 = -5.0000
- 2.Take absolute value: |-5.0000| = 5.0000
- 3.Divide by exact: 5.0000 / 100 = 0
- 4.Multiply by 100: 0 × 100 = 0%
Percentage Error Calculator: key facts
- What it does
- Calculate percentage, absolute, and relative error
- Category
- Math Calculators
- Cost
- Free, with no account, sign-up, or install.
- Your data
- Runs entirely in your browser — the files and text you enter are never uploaded to a server.
- Last reviewed
- . Report an incorrect result.
What this tool is for
Percentage error tells you how far off a measurement or estimate is from the true value, as a proportion — the standard way to express accuracy in science and engineering. This calculator takes the exact value and the approximate value and returns the percentage error, along with the absolute and relative error behind it.
Students use it to grade the accuracy of lab measurements; anyone comparing an estimate to a known figure uses it to quantify how close they got. By breaking out absolute and relative error too, it shows the full chain from raw difference to final percentage, and it handles the awkward case where the exact value is zero gracefully.
How to use the Percentage Error Calculator
- Enter the exact (true) value.
- Enter the approximate (measured or estimated) value.
- Read the percentage error.
- Review the absolute error and relative error shown in the step-by-step breakdown.
Absolute, relative, and percentage error
The tool reports three related quantities from the same pair of numbers. Absolute error is the size of the discrepancy in the original units. Relative error divides that by the exact value, producing a dimensionless proportion. Percentage error is the relative error expressed per hundred.
Taking the absolute value is what makes the result a magnitude rather than a direction, so a measurement that is too high and one that is too low by the same amount report identical error. The step-by-step working preserves the signed difference before the absolute value is applied, so you can still see which way the measurement went wrong.
The division is by the exact value, not by the measurement. That convention matters because it makes the error a fraction of the truth rather than a fraction of the guess.
- The defaults — an exact value of 100 measured as 95 — give an absolute error of 5, a relative error of 0.05, and a percentage error of 5%.
- An absolute error of 5 against an exact value of 10,000 is only 0.05% — the same absolute discrepancy, a very different quality of measurement.
- Measuring 102 instead of 95 reports the same 2% error magnitude as measuring 98, since direction is discarded.
What the Percentage Error Calculator gets right
- It reports all three related figures — percentage error, absolute error, and relative error — so you see how the final percentage is derived.
- It uses the standard formula, taking the absolute difference over the true value, so signs never distort the result.
- It handles a zero exact value gracefully, showing the absolute error rather than producing a division error.
- Calculations are instant and run locally with no account.
Accuracy, precision, and significant figures
Percentage error measures accuracy — closeness to the true value. It says nothing about precision, which is the repeatability of a measurement. An instrument can be highly precise and consistently wrong, giving the same reading every time with a large systematic error, and this calculation would flag that while repeated measurements alone would not.
The distinction between error types is worth carrying. Systematic error shifts every reading the same way and comes from miscalibration or flawed method; it can be corrected once identified. Random error scatters readings around the true value and is reduced by averaging repeated measurements. Percentage error against a known standard is the usual way to detect the systematic kind.
Reporting matters too. An error quoted to more significant figures than the underlying measurement justifies implies precision that is not there, so round the result to match your data. And when the exact value is zero, percentage error is undefined — no meaningful proportion exists — which is why absolute error is the appropriate measure in that case.
Frequently Asked Questions
How is percentage error calculated?
It is the absolute difference between the approximate and exact values, divided by the absolute exact value, multiplied by 100. For an exact value of 100 and an approximate of 95, the percentage error is |95−100| ÷ 100 × 100 = 5%.
What is the difference between absolute and relative error?
Absolute error is the raw difference between the measured and true values, in the original units. Relative error is that difference divided by the true value, a unitless ratio. Percentage error is simply the relative error expressed as a percentage.
Why can't I use an exact value of zero?
Percentage and relative error require dividing by the exact value, and division by zero is undefined. When the exact value is zero, this calculator shows the absolute error instead, since a meaningful percentage cannot be computed.
What counts as a good percentage error?
It depends entirely on context — a low percentage error means the approximation is close to the true value. Many school labs treat under 5% as good, but precision fields demand far smaller errors, while rough estimates may tolerate more. Lower is always better.
