Percentage Error Calculator
Compare a measured or estimated value against the accepted true value and express the error as a percentage. Common in science, engineering, and data analysis.
The Formula
The absolute value signs mean the result is always positive — it shows the magnitude of error, not direction. The true value is always the denominator.
Examples
Physics experiment: You measure the speed of sound at 340 m/s. The accepted value is 343 m/s.
|340 − 343| ÷ 343 × 100 = 0.87% error.
Forecast vs actual: You estimated 950 units sold; actual was 1,000.
|950 − 1,000| ÷ 1,000 × 100 = 5% error.
When to Use Percentage Error
Percentage error is used when one value is a known, accepted "truth" (a theoretical value, a standard, a target) and the other is an approximation or measurement. If neither value is the "true" one, use percentage difference instead.
Common Questions
Can percentage error be negative?
In the standard formula it's always positive. Some disciplines show sign to indicate whether the measurement was high or low — remove the absolute value to get a signed result.
What is an acceptable percentage error?
It depends on the field. In a school physics experiment, under 5% is typically good. In manufacturing, tolerances can be under 0.1%. There's no universal threshold.
Percentage error vs percentage difference — which should I use?
Use percentage error when one value is a known "true" value (like a standard or theoretical number). Use percentage difference when both values are measurements with no clear ground truth.