Percent Error & Percentage Difference Calculator

Percent error, percentage difference and percent change

These three measures all express how far apart two numbers are as a percentage, but they answer different questions. Percent error tells you how far a measured or estimated value is from the accepted true value: |measured − true| ÷ |true| × 100. It is the standard way to report accuracy in lab reports, where you compare your experimental result with a textbook constant such as the acceleration due to gravity or the boiling point of water.

Percentage difference is used when neither value is the reference — two measurements, two prices from different shops or two test results. It divides the absolute difference by the average of the two values: |A − B| ÷ ((|A| + |B|) ÷ 2) × 100, so swapping the values gives the same answer. Percent change describes growth or decline from an old value to a new one, (new − old) ÷ |old| × 100, and keeps its sign to show whether it went up or down.

Interpreting the result

A small percent error means a measurement is accurate, but what counts as small depends on the field. In an introductory physics lab a few percent is usually fine, while precision engineering may need errors well below 0.1 %. Percent error measures accuracy, not precision: repeated measurements that agree closely with each other can still all be wrong in the same way because of a calibration problem or a systematic error.

Be careful not to mix up the measures. A price rising from 50 to 75 is a 50 % change, but the percentage difference between 50 and 75 is 40 %, because it is measured against their average of 62.5. The calculator shows the absolute difference and the signed difference alongside the percentage, and prints the formula with your numbers so you can copy the working into a report. All calculations run locally in your browser.