Percent Error Calculator
This percent error calculator compares an experimental (measured) value with the accepted (true) value – optionally against a tolerance – and shows percent, absolute and relative error.
Source: Wolfram MathWorld – Relative error and percentage error. Updated: .
How it is calculated
Percent error = |measured value − accepted value| ÷ |accepted value| × 100%. If a student measures g as 9.6 m/s² instead of 9.81 m/s², the percent error is 0.21 ÷ 9.81 × 100% ≈ 2.14% (the measurement is 2.14% too low).
Absolute, relative and percent error
- Absolute error: Δ = measured − accepted, in the unit of the measurement (here −0.21 m/s²).
- Relative error: δ = Δ ÷ |accepted|, unitless (−0.0214).
- Percent error: |δ| × 100% (2.14%). The sign of Δ tells you whether you measured too high or too low.
Chemistry, physics and forecasting
In chemistry labs the “accepted value” is the theoretical yield or literature constant; in business it is the forecast or budget. Budget $50,000, actual $46,500 → (46,500 − 50,000) ÷ 50,000 = −7%. Add a tolerance (e.g. ±5%) to see instantly whether a result passes – handy for quality control and machining limits. Report the result with sensible significant figures.
Percent difference between two values
When neither number is the reference – two instruments, two quotes – use the symmetric percent difference: |A − B| ÷ ((A + B) ÷ 2) × 100%. For 40 and 60 that is 40%, in either order. The percent change from 40 to 60 would be +50% (and −33.3% the other way); for that, use the percentage calculator.
Tips
In Excel: =ABS(measured-accepted)/ABS(accepted), formatted as a percentage. Summarise repeated measurements first with the standard deviation calculator, and test whether a deviation is statistically significant with the p-value calculator.
Frequently asked questions
How do you calculate percent error?
Subtract the accepted value from the measured value, divide by the accepted value, take the absolute value and multiply by 100: |9.6 − 9.81| ÷ 9.81 × 100 ≈ 2.14%.
Can percent error be negative?
The percent error itself is usually given as a positive number. The signed version, (measured − accepted) ÷ accepted, is negative when the measurement is too low.
What is a good percent error?
It depends on the field: in school labs under 5% is usually fine, in precision measurement far less. Compare it with your measurement uncertainty.
What is the difference between percent error and percent difference?
Percent error compares against a known true value. Percent difference compares two measurements against their average, because neither is known to be correct.
How do I calculate percent error in Excel?
Use =ABS(B1-A1)/ABS(A1) with the accepted value in A1 and the measured value in B1, then format the cell as a percentage.
Sources and legal basis
- Wolfram MathWorld – Relative error and percentage error
- Wolfram MathWorld – Absolute error
- NIST Technical Note 1297 – Evaluating and expressing measurement uncertainty
As of:
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