Percent Error Calculator

Free Percent Error Calculator for Students

Our free Percent Error Calculator for Students uses the percent error formula (shown in Figure 01 below) to calculate how close a measured or estimated value is to an actual (or exact) value. The result is the difference between your measured valued and the actual value expressed as a percentage.

In terms of accuracy, the closer that a percent error calculation is to zero, the more reliable the result. And, conversely, the larger the percent error, the less accurate and/or reliable the measured value.

The percent error calculator above will use the following Percent Error Formula and it will automatically round the answer to the nearest hundredth of a percent.

The Percent Error Calculator Formula:

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

This scientific tool for measuring and assessing the accuracy of measurements and predictions can be extremely useful whenever you are comparing and analyzing the results of measurements or making predictions.

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).

Percent Error Calculator: How Does the Formula Work?

While our free percent error calculator is a handy tool for making quick and accurate calculations, you can also easily find percent error by using the percent error formula.

Whenever you know the measured value and the actual value of a situation, you can solve problems by using the percent error formula.

Now, let’s work through two step-by-step examples of how to find percent error using the percent error formula.

Example #1: Finding Percent Error

Let’s consider the following scenario for our first example:

Scenario: Katy estimated that there are 600 students in her graduating class. However, according to the enrollment logs, her graduating class has 642 students.

What is the percent error?

In this case, we know that…

Measured Value: 600
Actual Value: 1642

Percent Error = [ ( | 600 – 642 | ) / 642 ] x 100

Step 2: Next, we have to evaluate the formula as follows:

= [ ( | 600 – 642 | ) / 642 ] x 100
= [ ( | -42 | ) / 642 ] x 100
= (42 / 642) x 100
= 6.542056

Step 3: Express your answer as a percentage.

Now we just have to rewrite 6.542056 as a percentage and round our answer to the nearest hundredth decimal place.

Final Answer: The percent error is 6.54%

Example #2: Finding Percent Error

For this example, we are dealing with the following situation:

Scenario: A chemistry student calculated the density of a substance to be 1.08 g/cm³. However, after using calibrated measurement tools, she found out that the exact density of the substance is 1.12 g/cm³.

What is the percent error?

As long as you know the percent error formula, you can solve this example as follows:

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

Step 1: Substitute the measured value and the actual values into the formula.

Measured Value: 1.08
Actual Value: 1.12

Percent Error = [ ( | 1.08 – 1.12 | ) / 1.12 ] x 100

Step 2: Next, we have to evaluate the formula as follows:

= [ ( | 1.08 – 1.12 | ) / 1.12 ] x 100
= [ ( | -0.4 | ) / 1.12 ] x 100
= (0.4 / 1.12) x 100
= 3.5714

Step 3: Express your answer as a percentage.

For the final step, we just have to take our result from Step 2 and express it as a percentage. In this case, we will round our answer to the nearest hundredths decimal place.

Final Answer: The percent error is 3.57%

If you take the measured value (1.08) and the actual value (1.12) from this example and input them into the percent error calculator above, you can verify that we have successfully solved this problem.

Whenever you are dealing with data and measurements related to scientific experiments, being accurate and precise is extremely important, as even the smallest of differences can have a huge effect on the results.

When is Percent Error Most Useful?

While percent error is a useful tool, it isn’t the right tool for every situation.

Percent error is useful whenever you are…

Comparing your results from an experiment to exact or generally accepted results.
Evaluating or assessing the accuracy of predicted results and or any calculations that you are testing against exact values.
Assessing the validity of a particular measurement method, technique, or tool.

However, if the actual or exact value is every zero (0), you will not be able to use the percent error formula or the percent error calculator, because you can not divide by zero when using the formula. In cases like this, your results will be undefined (making them useless).

Is Percent Error Every Negative?

Percent error is always positive. Remember that the percent error formula includes absolute value, which means that the result will always be a positive number expressed as a percentage. In the event that you end up with a negative answer, go back and work through the problem again to find your mistake.

When is Percent Error considered bad?

Whether or not a percent error can be considered good or bad depends on the situation. However, in a general sense, measurements with percent errors that are closer to zero (less than 5%) can be considered to be very accurate. However, measurements with a percent error greater than 9.9% start to become generally inaccurate and scientifically unreliable.

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