Percent Error Calculator
Find the percent error between an observed (measured) value and a true (expected) value. Results include absolute error, relative error, and percentage error with step-by-step math.
Modify the values and click Calculate.
Formula
Example: observed 10, true 11 → 9.09% error
Percentage error
Percentage error measures the discrepancy between an observed value (what you measured or calculated) and a true value (the accepted, expected, or theoretical value). It is widely used in science, engineering, and laboratory work to assess how close a measurement is to a known standard.
When comparing measured density to a reference value, or experimental acceleration due to gravity to the textbook constant, percent error tells you how far off your result is — as a percentage of the true value. Small percent error means your measurement is close; large percent error indicates a significant difference that may need investigation.
Errors can arise from human mistakes, estimation, instrument limitations, environmental factors, or rounding. Understanding percent error helps you judge whether results are reliable enough for your purpose.
Computing percentage error
Computing percentage error involves three steps:
- Find the absolute error — the absolute difference between observed and true values.
- Find the relative error — absolute error divided by the true value (usually the absolute value of the true value).
- Multiply the relative error by 100 to get percentage error.
Example: If the observed value is 56.891 and the true value is 62.327:
|56.891 − 62.327| ÷ 62.327 × 100% = 5.436 ÷ 62.327 × 100% = 8.722%
When the true value is unknown, scientists often use standard deviation or uncertainty ranges to describe error. See our standard deviation calculator for related statistics.
Negative percentage error
Standard percent error uses absolute value, so the result is always non-negative. However, if you omit the absolute value, you can get a signed percent error that indicates direction:
Example: Observed = 7, True = 9:
(7 − 9) ÷ 9 × 100% = −22.222%
A negative value means the observed measurement is smaller than the true value. Enable “Show signed percent error” in the calculator above to see this variant alongside the standard result.
How to use this calculator
- Enter your observed value (measured or experimental result).
- Enter the true value (accepted or theoretical value). It cannot be zero.
- Optionally check “signed percent error” to see directional error.
- Click Calculate to see percent error, absolute error, relative error, and steps.
Real-world examples
- Chemistry lab: Compare measured molar mass to the periodic-table value.
- Physics: Compare experimental g (9.78 m/s²) to standard g (9.81 m/s²).
- Manufacturing: Check if part dimensions fall within acceptable percent error of specifications.
- Forecasting: Compare predicted sales to actual sales using percentage change tools.