✅ Percent Error Calculator
Calculate the percentage difference between an experimental (observed) value and a theoretical (true) value.
Enter Values
Percent Error
0%
Absolute Error: 0
| (Obs - True) / True | × 100%
What is Percent Error?
Percent Error (or percentage error) expresses the difference between an estimated, measured, or experimental value and the exact, known, or theoretical value as a percentage. It is heavily used in chemistry, physics, and statistics to determine how accurate an experiment or measurement is.
The closer the percent error is to 0%, the more accurate your measurement is.
Percent Error Formula
The standard formula for calculating percent error uses the absolute value to ensure the percentage is always positive:
Percent Error = | (Observed Value − True Value) / True Value | × 100%
Where:
- Observed Value (Experimental Value): The number you measured, guessed, or calculated yourself.
- True Value (Theoretical / Accepted Value): The exact, factually correct, or widely accepted number.
- Absolute Error: The top part of the fraction |Observed - True|. It shows the raw difference without a positive/negative sign.
Example Calculation
Imagine you estimated that a concert would have 200 people (Observed Value), but the actual ticket sales showed 250 people attended (True Value).
- Subtract True from Observed: 200 − 250 = -50
- Take the Absolute Value: |-50| = 50 (This is your absolute error)
- Divide by the True Value: 50 / 250 = 0.20
- Multiply by 100 to get percentage: 0.20 × 100 = 20% error.
Frequently Asked Questions
Can percent error be negative? +
Technically, no. The official formula uses absolute value (the vertical bars | |) which forces the result to be positive. A positive percentage simply tells you the magnitude of the error. However, if you drop the absolute value bars, a negative result indicates your measurement was lower than the true value.
What is a good percent error? +
This depends on the context. In high school science labs, a percent error under 10% is usually considered excellent. In professional chemistry or manufacturing, the acceptable percent error might be less than 1% or even 0.1%.
What is the difference between percent error and percent difference? +
Percent error compares a measured value to an exact, known value. Percent difference compares two measured values where neither is considered the "true" value, by dividing their difference by their average.