Percent Error Formula

Percent Error Formula with Definition, Examples, and Percent Error Calculator

The Percent Error Formula

Percent error is a way of expressing how close an estimated or measured value is from the actual (or exact) value, and it is expressed as a percentage.

The smaller that a percent error value is, the closer a measured (or estimated) value is to the actual value (and vice versa). This tool for measuring accuracy is useful whenever you are comparing measurements, results, or predictions.

As long as you know the measured value and the actual value, you can easily calculate percent error using the Percent Error Formula:

• Percent Error = [ ( | Measured Value – Actual Value | ) / Actual Value ] x 100

Where:

• The measured value is a measurement, estimation, or prediction

• The actual value is the exact measurement or value.

• The absolute value bars ( | | ) indicate that the result must always be positive.

Note that the concept of Percent Error can sometimes be expressed using different names including the percentage error equation and the error percentage formula, but they actually all mean the same thing.

In the next section, we will walk through a step-by-step example of how to use the Percent Error Formula to solve a math problem.

How to Use the Percent Error Formula: Example

Now that you know the percent error formula, it’s time to learn how to use it correctly to solve problems.

Let’s gain some practice with using the formula by solving the following practice problem:

Example: Arnie estimated that his height is 57 inches. After measuring his height with a tape measurer, he learned that his actual height is 60 inches. What was the percent error of Arnie’s measurement?

In order to use the Percent Error Formula to solve this problem, we have to identify two key pieces of information:

• Measured Value: 57 inches

• Actual Value: 60 inches

Once we have identified the measured value (57) and the actual value (60), we can substitute these values into the Percent Error Formula and solve as follows:

• = [ ( | Measured Value – Actual Value | ) / Actual Value ] x 100

• = [ ( | 57 – 60 | ) / 60 ] x 100

• = [ ( | -3 | ) / 60 ] x 100

• = ( 3 / 60 ) x 100

• = .05 x 100 = 5

• = 5%

In review, se simply substituted 57 for the measured value and 60 for the actual value into the percent error formula and evaluated.

Final Answer: The percent error was 5%.

The entire step-by-step process for solving this problem is illustrated in Figure 01 below.

Percent Error Formula Reference Sheet and FAQs

If you are learning about how to calculate percent error on your own or in school, it can be incredible helpful to have a percent error formula reference sheet on hand whenever you are working on percent error practice problems.

To download your free Percent Error Formula Reference Sheet, click the text link below to download your free PDF file. We recommend keeping a copy in your math or science notebook for quick reference whenever you need to have access to the percent error formula.

• Click Here to Download Your Free Percent Error Formula Reference Sheet

Percent Error Formula FAQs

How can you explain the Percent Error Formula in one sentence?

The percent error formula represents the difference between the result that you found and the actual value, divided by the actual value, and expressed as a percentage (usually rounded to the nearest tenth of a percent).

Are percent error and percent difference the same thing?

No. While percent error is a comparison of a measured value and an exact value, percent difference is a comparison of two different measured or experimental values with no exact value involved.

Can the Percent Error ever be a negative number?

No. Since the percent error formula involves finding the absolute value of the difference between the measured value and the actual value, the result will always be a positive percentage. If you ever end up with a percent error that is negative, you should go back and work through the problem again, as you have surely made a mistake in your calculations.

What would be considered a “good” percent error?

While the answer to this question depends on the context of the situation, generally speaking, the closer that a percent error is to zero the more accurate the measured value is (compared to the true value). Typically, an percent error that is less than 5% could be considered excellent, while anything between 5-10% could be considered good. However, percent errors that are 10% are greater are usually not acceptable, as the measured data could be considered inaccurate and unreliable.

Percent Error Calculator

Make quick calculations or check your work by using our free Percent Error Calculator below.

Simply input the measured value and the actual value to get an instant percent error answer.

While we do not recommend that you rely on our free percent error calculator to solve all of your Percent Error practice problems, it can be a useful tool for making quickly calculations and for checking your answers to assess your understanding of how well you understand how to use the percent error formula.

If you need more help with finding percent error, check out our free How to Calculate Percent Error in 3 Easy Steps Student Guide, which includes a more in-depth review of Percent Error, as well as several step-by-step practice problems.

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