Formula
Error = measured value − accepted value. Absolute error = |measured value − accepted value|. Percent error = (absolute error ÷ |accepted value|) × 100. Signed percent error = ((measured value − accepted value) ÷ |accepted value|) × 100.
Math & Statistics
Percent Error Calculator
Calculate percent error between an experimental or measured value and an accepted reference value, with absolute and signed error shown clearly.
Calculator
Working calculator
Live result2.00% errorAbsolute error 2.00 · signed -2.00% (below reference)
Formula used
Error = measured value − accepted value. Absolute error = |measured value − accepted value|. Percent error = (absolute error ÷ |accepted value|) × 100. Signed percent error = ((measured value − accepted value) ÷ |accepted value|) × 100.
This is the method behind the answer, so the result can be checked rather than simply trusted.What-if check
Measured-value sensitivity
Move the measured value by one unit either side while keeping the accepted value fixed. This shows whether the error result is stable or sensitive to a small measurement change.
| Measured value | Raw error | Percent error |
|---|---|---|
| 97.00 | -3.00 | 3.00% |
| 98.00 | -2.00 | 2.00% |
| 99.00 | -1.00 | 1.00% |
Visual proof
Measured versus accepted
The bars keep the reference value visible so the percentage is not mistaken for a standalone score.
Printable calculation report
Result: 2.00% error. Assumption: The accepted/reference value is treated as the comparison base.
- Measured value
- 98
- Accepted/reference value
- 100
- Page/date context
- 2026-05-16 UTC page version
- Page URL
- https://calculationtime.com/calculators/percent-error-calculator
Worked example
Measured value = 98 and accepted value = 100. Error = 98 − 100 = −2. Absolute error = 2. Percent error = 2 ÷ 100 × 100 = 2.00%. Signed percent error is −2.00%, showing the measurement is below the reference.
Professional note
Master’s Tip: write down the source of the accepted value before judging the percent error. In labs, QA checks and estimating work, a small arithmetic error can still be unacceptable if the reference value, instrument tolerance or calibration method is wrong.
Regional and unit assumptions
Standard or basis: transparent relative-error arithmetic using the accepted value as the denominator. No laboratory, engineering or compliance standard is claimed unless the user supplies the governing tolerance separately.
Assumptions and limitations
- The accepted/reference value is treated as the comparison base.
- Percent error is undefined when the accepted value is zero because the formula would divide by zero.
- The main result uses absolute percent error so overestimates and underestimates are comparable.
- Signed percent error is shown to indicate whether the measured value is above or below the reference value.
- This is transparent general arithmetic; measurement uncertainty, calibration and laboratory method rules are not certified by this page.
Methodology & Accuracy
How this calculator is checked
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
Formula used
Error = measured value − accepted value. Absolute error = |measured value − accepted value|. Percent error = (absolute error ÷ |accepted value|) × 100. Signed percent error = ((measured value − accepted value) ÷ |accepted value|) × 100.
Standard or basis
Standard or basis: transparent relative-error arithmetic using the accepted value as the denominator. No laboratory, engineering or compliance standard is claimed unless the user supplies the governing tolerance separately.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master's Tip
Master’s Tip: write down the source of the accepted value before judging the percent error. In labs, QA checks and estimating work, a small arithmetic error can still be unacceptable if the reference value, instrument tolerance or calibration method is wrong.
Related calculators
Questions
What is percent error?
Percent error expresses the absolute difference between a measured value and an accepted value as a percentage of the accepted value.
What is the percent error formula?
Percent error = |measured value − accepted value| ÷ |accepted value| × 100.
Why does the calculator show signed error too?
Absolute percent error shows size. Signed percent error also shows direction, so you can see whether the measured value is above or below the reference.
Can accepted value be zero?
No under the standard percent-error formula. Dividing by zero is undefined, so use an absolute error or another comparison method when the reference value is zero.
Is percent error the same as percent change?
No. Percent error compares a measured value with an accepted reference value. Percent change compares a new value with an original baseline.
Calculation note
Percent error is common in science classes, quality checks, estimating and measurement work because it turns a raw difference into a relative comparison. The arithmetic is simple, but the accepted reference value and tolerance rule decide whether the error is meaningful.
Relative error depends on the reference value
A difference of 2 units can be small or large depending on the accepted value. Two units away from 100 is a 2% error, while two units away from 10 is a 20% error. That is why the denominator is visible in the calculator.
Absolute size and direction answer different questions
Many classroom formulas report absolute percent error so overestimates and underestimates can be compared by size. The signed result is still useful because it shows whether the measured value is above or below the reference.
Arithmetic does not replace uncertainty or calibration
Percent error can highlight the gap between a result and a reference, but it does not prove why the gap happened. Real measurement work may require uncertainty budgets, calibration checks, repeat measurements and a defined tolerance rule.