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Programmers and Teachers:

# Percent Error Calculator

## Lesson on Percent Error

#### Lesson Contents

### Why do we Calculate the Percent Error?

**Percent error gives us the percentage of inaccuracy from the exact/true value.** This inaccuracy of a measured/approximated value is very important in mathematics, science, statistics, and engineering. If the measured/approximated value is equal to the exact/true value, there is zero error. If it is not equal to the exact/true value, we use the percent error formula.

The formula for finding percent error is given as:

The operation of multiplying by 100% converts from decimal form of error to percentage form of error. We use absolute value bars around the fraction because the approximate value may be either greater or less than the exact value, and the exact value may be positive or negative. By taking the absolute value of the entire fraction, we ensure the percent error is a positive value.

Depending on the situation, we may not have access to an exact value. In that case, we may use the theoretical value in place of the exact value. The formula will still function correctly.

### Example Problem

An airplane’s airspeed sensor is being tested in a wind tunnel which is operating at a known airspeed of 45 m/s. The sensor outputs a measured airspeed of 47.3 m/s. What is the percent error of the airspeed sensor?

Solution:

1.) We have all values needed to apply the percent error formula.

2.) Plugging into the formula, we get:

PE = |^{(exact value – approximate value)}⁄_{(exact value)}|×100%

PE = |^{(45 – 47.3)}⁄_{(45)}|×100% = |(-0.05111)|×100% = 5.111%

3.) **The percent error of the airspeed sensor is 5.111%.**

## How the Calculator Works

The calculator on this page uses the formula shown above to calculate the percent error just as we would if calculating it by hand. The calculator enjoys the advantage of having a computer processor for number crunching.

Your inputted approximated value and exact value are sent to the program and put through the percent error equation. The answer is then sent back to this page and displayed.