Percent Error Calculator
Percent error tells you how far a measured result deviates from a known true value, expressed as a percentage of that true value. It is the standard accuracy metric in science, engineering, and quality control because it scales the difference relative to the size of the reference value, making comparisons meaningful across very different measurement scales. A result of 1% means you were extremely close; 20% means your reading was well off. The formula takes the absolute difference between your experimental and theoretical values, divides by the absolute theoretical value, and multiplies by one hundred. What the raw number does not tell you on its own is whether your reading ran high or low, and how much of the true value you actually captured. This calculator returns all four figures at once. Enter the value you recorded (the experimental value) and the accepted or expected value (the theoretical value). Both can be positive or negative decimals, as long as the theoretical value is not zero. You get back the percent error, the raw absolute difference between the two values, the direction of the deviation (over or under, and by how much), and your relative accuracy as a complement percentage. The tool suits students writing up science experiment results, technicians validating instrument calibration, engineers assessing production tolerances, and anyone comparing an observed figure against a published benchmark. Results are for reference only.
How it works
The calculator applies the standard percent error formula: % Error = (|Experimental − Theoretical| ÷ |Theoretical|) × 100. Absolute value signs around the numerator and denominator mean the result is always a positive number regardless of which input is larger. Absolute error is the raw arithmetic difference between the two values before the percentage conversion. Direction compares the inputs directly: if the experimental value exceeds the theoretical value, the measurement ran over; if it falls short, it ran under. Relative accuracy is the complement of percent error, calculated as 100% minus the percent error, giving an at-a-glance measure of how much of the true value your reading captured.
Worked example
You weigh a 100-unit reference standard on a laboratory scale and the readout shows 95. The absolute error is |95 − 100| = 5. Percent error is (5 ÷ 100) × 100 = 5.00%. The reading was under the true value by 5.00 units and relative accuracy is 95.00%. These match the default values pre-filled in the calculator above, so you can verify the output without changing anything.
Related calculators
- Absolute Error Calculator: find the raw difference between a measured and true value without converting it to a percentage.
- Relative Error Calculator: express error as a decimal ratio rather than a percentage, useful when comparing measurements across different units.
- Measurement Uncertainty Calculator: quantify the range of possible values around a repeated measurement set.
- Significant Figures Calculator: round a result to the correct number of significant figures before quoting or comparing values.