Percent Error Calculator

Percent error measures the difference between an observed (experimental) value and a true (accepted) value, expressed as a percentage of the true value. The underlying formula is defined as: Percent Error = ((Observed Value - True Value) / True Value) * 100. If the result is negative, it indicates that your observed value under-shot the true value. Conversely, a positive percentage means the observed value overshot the true measurement. In many laboratory settings, the absolute value is taken to focus strictly on the magnitude of the deviation rather than its directional sign.

Imagine you are conducting a chemistry experiment to determine the density of a metal object. Your analytical balance and water displacement method yield an observed density of 2.75 grams per cubic centimeter. However, the theoretical true density listed in your handbook is 2.70 grams per cubic centimeter. To find your percent error, first subtract the true value from the observed value: 2.75 - 2.70 = 0.05. Next, divide this difference by the true value: 0.05 / 2.70 = 0.018518. Finally, multiply by 100 to convert the decimal into a percentage, yielding a percent error of approximately 1.85%.

When recording measurements, always maintain consistent significant figures across your observed and true values to prevent artificial precision distortions. Be mindful of the difference between percent error and percent difference; percent error compares an experiment against a known standard, whereas percent difference compares two distinct experimental measurements. Always double-check whether your specific application requires the signed directional error or the absolute magnitude of the error.