Introduction to Percent Error

As the title says, percent error is presented in a percentage format. It indicates the variation between the estimated and the real value of a calculation. Consider this example for better understanding. Let's say the actual distance between two cities is 85km, but after calculating, we get a distance of 80km.

Here, the percent error is 5%. To figure out the percent error, we have to find the difference between the estimated and real answer, and then divide it by the real answer. By identifying the percent error, we can understand the severity of the mistake made while calculating. 

When we find the percent error, we can understand the impact these errors cause in the results calculated. The formula for percent error is:

Percent error = (Measured value - True value) / True value × 100

Here, the measured value is the result we get through the calculation. True value is the established value.

Look at this example that shows how the formula works:

The measured value of a machine is 50 cm. But the actual (true) value of the machine is 48 cm. Now let us calculate the percent error.

The formula for percent error calculation is:

Percent error = (Measured value - True value) / True value × 100

Percent error = (50 - 48) / 48 × 100
 

First, subtract the true value from the measured value:

50 - 48 = 2
 

Next, divide 2 by the true value:

2 / 48 = 0.0416

Now, we can multiply 0.0416 by 100:

0.0416 × 100 = 4.16

Thus, the percent error is 4.16%. 
 

Percent error calculation is a simple method to find the variation between two values, one is the experimental value, and the other is the actual value. Percent error is a commonly used concept in various fields to estimate the accuracy of results. By following three steps we can find the percent error. They are listed below:

Step 1: Subtract the measured value from the actual value. The answer is known as an absolute error.  Also, remember to avoid negative signs(-). 

Step 2: Divide the error by the actual value. It gives a value and it is known as the relative error.

Step 3: Multiply the value by 100. 

These three steps help us determine the percent error of a calculation or experiment.  
 

As we know, most of today’s innovations are the result of experiments conducted thousands of years ago. To introduce new concepts and theories, scientists and mathematicians employed several methods. Percent error is a vital concept in science and mathematics.

It helps scientists, researchers, and engineers to find and analyze how credible their results are. In the early days, researchers compared their experimental results with the established values. A Greek mathematician named Eratosthenes evaluated the error made while calculating the Earth’s circumference in relation to the real value (the actual circumference).

This illustrated a simple method of percent error calculation.  Over time, percent error calculation has been commonly used by researchers.  In the modern era, percent error is frequently used in various fields such as engineering, physics, chemistry, economics, and so on. 
 

When calculating data, the results can be different from the actual answers. To solve this problem, we use percent error to analyze the error and the accuracy of the answer. Students who focus on laboratory research can determine how far their experimental values match the actual values.

Percent error helps identify inconsistencies after an experiment, allowing students to correct mistakes in future trials. In the field of medical science, percent error plays a vital role. It is used to check the specific standards of products in manufacturing sectors and to assess the accuracy of measurements in engineering. 

To assess the precision of measurements in a calculation or an experiment, researchers use the key concept of percent error. It helps analyze result reliability. Understanding the various types of percent error will enable students to achieve accurate results. The different types of percent errors are explained in detail.

Absolute percent error:

An absolute percent error calculates the difference between a measured value and the true value. It ignores the degree of measured and true value. It doesn’t consider whether the measured values are greater or lower than the actual value. To find the absolute error, we can use the formula:

Measured Value - True Value = Absolute Error. 
 

For example, if percent error = (50 - 48) / 48 × 100

The absolute value is 2(50 - 48 = 2).

Relative percent error:

The relative percent error focuses on the error’s relative size. It compares the error to the measured value. When comparing different types of errors in calculations, relative percent error is helpful. 

For example, if percent error = (12.4 - 12.0) / 12.0 × 100

The relative percent error = (measured value - true value) / true value 

Percent error = (12.4 - 12.0) / 12.0 = 0.033

Percent error in experimental value:

It analyses the difference between experimental values and the expected values. This is commonly used in the field of experimental science, where professionals need to know how much the supposed value deviates from the true value. 

For example, Percent error = (Experimental value - True value) / True value × 100

Percent error in the measurements of constants:

When we measure the speed of light or the gravity acceleration, the percent error indicates how close the measured value is to the actual value.

For example,
Percent error = (Measured constant value - Known constant value) / Known constant value × 100.



 

Determining how close the measured value is to the actual value helps students analyze the accuracy of their calculations. Following some tips and tricks will help kids to improve their knowledge of percent error calculation. Here, some of the tips and tricks are listed.

• Don't consider the negative sign in the calculation. If you get a negative result, consider it as a positive answer. For example, if you get -1.4, consider it as 1.4. The negative sign is ignored because percent error is always about the immensity of the error, not its direction.
   
• Be careful to apply the correct formula for percent error calculation. The denominator will be the true value. Use the proper values for each term.
   
• To get the final values as a percentage, multiply the value by 100. This converts a decimal into a percentage. 
   
• Double-check the values to find the highest percent error. The large percent error indicates a major mistake in the calculation.
   

• Measured value: It is the value obtained from an experiment or calculation. Sometimes the value may contain errors and it will lead to incorrect results.  

• True value: It is the established value or the actual value in a calculation or experiment. To ensure the accuracy of the measured value, the true value is used as a reference. 

• Percent error: It is the absolute difference between the estimated value and the actual value. The difference is divided by the actual value and the answer is multiplied by 100 to denote it as a percentage. 

• Absolute percent error: It measures the difference between a measured value and the actual value. To calculate the absolute percent error we have to subtract the measured value from the actual value.