How To Calculate Percent Error

John Millar Published On May 22, 2021 | Updated on Dec 28, 2023 Writing Service

What Is Percent Error?

Percent or percentage error is calculated to learn the difference of the measured value from the actual value.

While measuring data, the final result varies due to human errors or manufacturing error in measuring instruments. Therefore, we use a percent error formula to calculate how close the measured value to the actual value is.

The formula to calculate percent error is:

Percentage Error = [(Experimental (Approximate) Value – Theoretical (Actual) Value) / Actual Value] × 100%

Percent Error: Key Guidelines

Can percent error be negative? Yes, when the experimental value is less than the theoretical value, the percent error becomes negative.

Here are some additional guidelines for calculating percent error using the formula.

The percent error is calculated to determine the difference between approximate values and exact values.
In some fields, percent error calculation is expressed as a positive number, while in others, either positive or negative value is accepted. The sign is kept to check if the recorded result falls above or below the actual value.
Even though absolute and relative errors are common, calculating percent error is a part of broader error analysis.
For accurate percent error calculation, it’s crucial to know to use the signs correctly and report the values using the correct number of the figures.

Percent Error Formula

According to the percent error definition, the difference between a measured value and a known value, divided by a known value, multiplied by 100%. For most applications, it is expressed as a positive value. But when calculating the percent error for chemistry or other sciences, it’s necessary to keep a negative value.

For example, let's assume you want to measure water's boiling point, and your result shows 101.5°C, which is your approximate value. But the actual boiling point of water is 100°C.

What is the percentage error between E (experimental value) = 101.5°C and T (theoretical value) = 100°C?

Insert digits in the percentage error formula for chemistry:

|E−T||T|×100
= (101.5−100) |100|×100
=1.5100×100
=0.015×100
=1.5%
=1.5% error

Note: The “|” symbol stands for absolute value, where negatives become positive.

How To Calculate Percent Error – Crucial Steps

If you wonder how to find percent error, these following steps will certainly help you understand the basic steps.

Subtract one value from another to get the ‘error’ value. The order would remain unchanged even if you miss the sign. However, if you leave the subtraction sign, subtract the actual value from the approximate value to get the ‘error.’
Divide the 'error' value by the known value to get a decimal number.
Now multiply the decimal value with 100 for a % value.
Add the % symbol to the result for the percent error.

Examples Of Percent Error Using The Formula

Example 1:

You know the accepted distance to the moon is 238,855 miles. But you measure it as 249,200 miles.

What would be your percent error?

Solution:

Experimental value = 249,200 miles
Theoretical value = 238,855 miles
Percent Error Formula = (Experimental Value – Theoretical Value / Theoretical Value × 100)
Percent Error= 249,200 – 238,855 / 238,855 x 100
= 4.33%

Example 2:

Let’s say you have the measurements of a copper cube, and you have to measure the cube's density using the given measurements. However, your result shows 8.78 grams/cm3 when the accepted measure is 8.96 grams/cm3.

What’s the percent error?

Solution:

Experimental value = 8.78 grams/cm3
Theoretical value = 8.96 grams/cm3
Percent Error Formula = (Experimental Value – Theoretical Value / Theoretical Value × 100)
Percent Error= 8.78 – 8.96 / 8.96 x 100
= 0.02%

Example 3:

How would you calculate the percent error of a weather forecast of 20 mm of rain when it was 25 mm in reality?

Solution:

Experimental value = 20 mm
Theoretical value = 25 mm
Percent Error Formula = (Experimental Value – Theoretical Value / Theoretical Value × 100)
Percent Error= 20 – 25 / 25 x 100

= -20% Percent Error Calculator

A percent error calculator is an online tool that calculates the percent error between an experimental value and a theoretical value. With this device, you can calculate the percent error within seconds and get do my math homework services.

This percent error calculator is widely prevalent among students in the US for accessibility. Follow these steps to find answers to your percent error equations.

Step 1: Enter the values in the empty box with ‘Experimental’ and ‘Theoretical’ texts.

Step 2: Crosscheck the numbers and click on the ‘Calculate’ option

Step 3: Voila! Your answer is ready for copy-paste.

Why Should I Use A Percent Error Calculator Online?

Many hesitate to use tools such as a percent error calculator, fearing accuracy. Therefore, we’ve compiled a few reasons why you must use the tool to calculate percent error right away.

Accurate results

Most students don’t use an online calculator for percent error because of inaccuracies. However, these tools are upgraded with an advanced algorithm that ensures accurate results.

No pressure

There’s no room for additional stress for calculating percent error if you use the calculator. You can wrap up your calculation quickly and get back to other tasks.

Quality Assistance

Even if you don't know the steps for solving an equation, you can use the percent error calculator to get 100% accurate results.

No downloads

You don’t have to download any software for using the tool, as you can complete it online itself.

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