Percent Error Calculator

Percent error is a measurement of the discrepancy between an observed (experimental) value and a true (accepted) value, expressed as a percentage of the true value. It tells you how far off your measurement is relative to what the actual value should be. A small percent error means your measurement was close to the true value; a large percent error means it deviated significantly.

The standard formula is: Percent Error = (|Experimental − Accepted| / |Accepted|) × 100%. The absolute value ensures the result is always positive unless you specifically want the signed version to indicate direction (over or under).

First, find the difference between your experimental and accepted values. Second, take the absolute value of that difference. Third, divide by the absolute value of the accepted value. Finally, multiply by 100 to convert to a percentage. For example, if you measured 9.65 m/s² and the accepted value is 9.80665 m/s², percent error = (|9.65 − 9.80665| / 9.80665) × 100 ≈ 1.5972%.

Percent error compares an experimental value to a known, accepted reference value. Percent difference is used when you have two measured values and neither is considered the 'true' value — it divides by the average of the two values instead. Use percent error in lab settings where a true value is known, and percent difference when comparing two independent measurements.

The standard percent error calculation uses absolute value and is always reported as a positive number. However, the signed version can be negative when your experimental value is less than the accepted value, which indicates you underestimated. This is useful when the direction of error (over vs. under) matters for your analysis.

What counts as acceptable depends entirely on the context. In many high school or undergraduate physics labs, percent errors under 5% are generally considered acceptable. In chemistry or engineering applications, tolerances may be much tighter — sometimes under 1%. Always refer to your specific experimental guidelines or industry standards to determine acceptability.

Percent error can arise from many sources including human measurement error, instrument limitations or calibration issues, environmental factors (temperature, pressure), rounding during calculations, and assumptions in theoretical models. Identifying the source of error is as important as quantifying it.

Absolute error is simply the difference between the experimental and accepted values (|Experimental − Accepted|) expressed in the original units of measurement. Percent error normalizes this by dividing by the accepted value and multiplying by 100, making it a dimensionless percentage. Percent error is more useful for comparing accuracy across different measurements or scales.