# Percent Error Formula: Rules and Examples

We’re now ready to take the percentage error formula out for a test drive.

### Example 1

Let’s say you’re a bookworm with a long vacation coming up. You go to the library to grab some reading material. Before you open the front door, you assume you’ll check out three books. But instead, for whatever reason, you only take home two books. What’s the percentage error of your estimate?

In our example, the experimental value is 3 and the actual value is 2. Plug in the numbers, and you get this:

Percent Error = (3 – 2)/2 x 100

If you’re old enough to read this article, we’re guessing you already knew that 3 minus 2 equals 1. Which leaves us with:

Percent Error = 1/2 x 100

Divide 1 by 2 and you get the following:

Percent Error = 0.5 x 100

And 100 times 0.5 equals 50. But remember, we have to express our final answer as a percentage. When we do that, we learn the original guess you made had a percent error of 50%.

This example was all about quantity (ie, the number of library books). But the percent error formula can also be applied to lots of other values ​​- like speed, distance, mass and time.

Bearing that in mind, let’s go through the formula again.

### Example 2

Suppose a college athlete thinks he’ll need 45 seconds to finish a hardcore workout challenge. But when he hits the gym, the routine takes him 60 seconds to complete. What was the percent error of the time estimate he started out with (45 seconds)?

Percent error = (45 – 60)/60 x 100

Right off the bat, we’ve hit a complication. If you subtract 60 from 45, you get a negative number (-15 to be exact).

Divide -15 by 60 and you’ll get -0.25, which is another negative value. And we can’t stop there; we still need to multiply the -0.25 by 100, giving us an answer of -25. Does that mean the percent error is -25%?

The percent error between an estimated value and the actual value cannot be expressed as a negative. It’s always written out as a positive value, whether the starting estimate was way too big or way too small.

Here’s where our old friends “absolute error” and “relative error” come into play. The value of -15 is only the relative error. You need to take the absolute value of that before proceeding with the calculation. Once you have the absolute error of 15, you can divide that by 60 and multiply by 100 for a percent error of 25%.