## How to Calculate Percent Error

It is often helpful to know exactly HOW accurate your measurements are. One way that you can do this is by calculating how much **error** there is in the measurements. The word error just means a mistake or deviation from what is expected, but there is a way that we can quantify exactly how much error there is in a measurement. This is called **percent error**, and it is a ratio of the difference between the true value of your measurement and the true value. This ratio is then multiplied by 100 to make it a percent.

Notice that the numerator in this expression is enclosed by two absolute value symbols (they look like this: | ). This means that what is inside these symbols should always be made positive.

Now, let's go back to the problem of my too-large rug. When I measured the size of my room, I got that it was 9 ft wide. However, the actual width of my room was 7.5 ft. What was the percent error in my measurement?

I really didn't do a very good job of making accurate measurements, did I? My measurement was 20% bigger than the actual size of the room. I guess that's why my new rug didn't fit!

What would happen if your measurement was SMALLER than the true value instead of larger? Let's look at an example of that too. Suppose that in a science experiment, you measure the acceleration of a falling ball to be 8.7 m/s2. You know that the true value of the acceleration due to gravity on Earth is 9.8 m/s2.

Did you notice that the percent error was still positive? In this calculation, you should always use the *absolute value* of the quantity in the numerator. Whether the measurement is bigger than the true value or the true value is bigger than the measurements, the percent error should still be positive.

## Lesson Summary

**Accuracy** is defined as how close a measurement is to the true or accepted value. It is important to make accurate measurements, and often, you may need to know exactly HOW accurate your measurements are. The amount of **error** in a measurement can be quantified by calculating the **percent error** between the measurement and the true or accepted value.