Percent Error Calculator

Percent error compares an experimental (measured) value to a known, accepted theoretical value (the true value). Percent difference compares two experimental values when neither is known to be the correct or true value (it uses the average of the two as the denominator).

By standard mathematical definition, percent error uses absolute value, meaning it is always positive. However, in some laboratory settings, the absolute value is omitted to show whether the measured value was higher (positive error) or lower (negative error) than the true value.

In student laboratory settings, a percent error under 5% is generally considered excellent, while 5% to 10% is acceptable. In professional high-precision research (like physics or metrology), acceptable margins are often much tighter—frequently under 0.1% or even parts per million.

If the theoretical value is exactly zero, the standard percent error formula divides by zero, which is undefined. In such cases, you should report the absolute error (the difference between the values) instead of a percentage.

To maintain high scientific accuracy, perform all intermediate calculations with full precision and only round the final percentage to the appropriate number of significant figures, matching the precision of your original measurements.