How to Calculate Percent Error: Tips and Applications

By Indeed Editorial Team

Published June 17, 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Science and mathematics are complex disciplines that use a variety of precise calculations. Percent error is one such calculation that allows scientists and engineers to determine the accuracy of a measurement. Understanding how to calculate percent error helps you to improve the accuracy of your measurements. In this article, we explain how to calculate percent error using a formula that expresses it as a relationship between absolute and real value, provide its applications, and highlight tips for calculating it.

How to calculate percent error

Here's how to calculate percent error, along with an example:

1. Decide on your approximate value

You may also refer to the approximate value as the estimated or experimental value. This is the value you receive from estimating, performing your initial calculations, or other means. For example, if you guess that there are 20 total strawberries in a case from the farmer's market, that becomes your approximate value.

Related: What Is Quantitative Analysis?

2. Determine the exact value

The exact value is the accepted value of a measurement that has already taken place. Using the same example from the market, the farmer could have a process to ensure she includes 18 strawberries in every package. You may discover this by opening the package of strawberries and counting how many are in there. The exact value of strawberries is 18.

3. Subtract the two figures

Subtract the exact value from your estimated one using the percent error formula. In the strawberries example, you can subtract 18, the real number of strawberries, from 20, the number of strawberries you think the farmer has included in the pack. Performing this calculation following the formula results in |-2|. This value tells you the difference between the real and estimated values and how far your guess was from the exact number.

4. Find the absolute value

Part of the percent error formula includes symbols that show absolute value. This means that even if your subtraction reveals a negative number, you can disregard the negative sign and only accept the absolute value of the number. In the same example, the absolute value of |-2| is two. These symbols only change a negative number from negative to positive, but if the calculation results in a positive number, then the value wouldn't change.

The absolute value symbols are a part of the equation because, for the percent error calculation, whether your estimate was over or under the exact value is usually irrelevant. The vital thing to know is how far removed from the actual value of your estimation was.

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5. Divide the absolute value by the exact value

Now that you know the absolute value and the exact value, divide the absolute value by the exact value. In the example, this means 2 / 18 = 0.11, where two is the absolute value calculation, and 18 is the exact number of strawberries in each package.

6. Decide how many decimal points you require

Your calculations at this stage may likely result in a long decimal number. While each need is different, you may use two numbers after the decimal point in your calculations most of the time. Your total calculation may be incorrect if you use too many or too few figures after the decimal point when you're rounding.

7. Multiply your decimal by 100

To convert your decimal result into a percentage, multiply it by 100 and add the percentage sign. In the strawberry example, 0.11 x 100 = 11, including the percentage symbol, makes it 11%. This means that your estimation of the number of strawberries in the pack was off by two strawberries, or 11% of the total real value of the strawberry package.

8. Confirm your calculations are accurate

To prevent inaccurate calculations, confirm that your work is complete and correct. If you forget to convert any negative figure to an absolute value and make it positive, the following calculations may continue to be negative and potentially incorrect.

9. Remove the absolute value symbols

There are situations where you may not want to use the absolute value symbols because you desire to retain the possibility of getting a negative result. This is typically the process for calculations in science when you want to measure the consistency of your recorded values versus your expected numbers. Here, your percent error formula may be:

Percent error = [Approximate value - Real value] / Real value x 100%

Applications of percent error

Percent error is a useful concept in science and math because it allows you to express how an experimental value disagrees with the actual or expected value. It can help you understand whether a recorded value falls within what you would consider the normal range for that measurement. You can also use it to compare different measurements with one another. Here are some real-life examples of where you might use percent error:

Estimating the number of people in a room

If you want to estimate how many people are in a room, but you only have a small sampling of the total population, you can use percent error to help you understand the potential range of values for your estimate. For example, let's say you want to estimate how many people are in a room, but you only know there are 50 chairs.

You could assume that each person needs one chair, so your estimate may be 50 people. Not everyone in the room is likely using a chair, and some people may share chairs, so your estimate could be off by a significant amount. To account for this possibility, you can use percent error to give you a sense of the range of values your estimate could be.

Measuring the consistency of recorded data

If you're conducting an experiment and recording data, you can use percent error to help you understand the consistency of your measurements. For example, if you're measuring the temperature of a chemical reaction over time, you expect the temperature to grow. If your recorded data shows that the temperature is decreasing, percent error can help you understand whether this is a consistent trend or if there was a mistake in your measurements.

Comparing two measurements to each other

You can also use percent error to compare two different measurements. For example, suppose you're measuring the height of a building and may want to know how accurate your measurement is. You could take a second measurement and then use percent error to see how close the two measurements are.

Determining the accuracy of a scientific instrument

If you're using a scientific instrument, such as a microscope or a thermometer, you can use percent error to help you understand the precision of your measurements. For example, suppose you're using a microscope to measure the size of a cell, and you want to know how accurate your measurement is. You could take a second measurement with a different microscope and then use percent error to see how close the two measurements are.

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Estimating the amount of material in a sample

If you're working with a small sample of material, you can use percent error to help you estimate the amount of material in the sample. For example, suppose you have a sample of soil that you want to analyze for metal content. You only have a small amount of the sample, and you don't want to waste any of it. You could use percent error to help you estimate the amount of metal in the sample, and then you can use that information to determine how much of the sample to use for your analysis.

Percent error in relation to absolute and relative error

You may see the absolute and relative errors mentioned alongside percent errors in a report or experiment because they are both part of the percent error formula or calculation steps. Absolute error is the difference between the hypothesized and the exact value, whereas relative error is when you divide the absolute error by the exact value. For example, you get your percent error by multiplying the relative error by 100%.

Tips for calculating percent error

Here are some tips to help you get the most accurate result when calculating percent error:

  • Use a consistent unit of measurement: When you're taking measurements, it's important to use a consistent unit of measurement. For example, if you're measuring the temperature of a chemical reaction, make sure that all of your measurements are degrees Celsius.

  • Take multiple measurements: If you're able to, take multiple measurements of the quantity. This may help you get a more accurate result, and it may also give you an idea of the range of values that your measurement could be.

  • Use the highest possible precision: When using a scientific instrument, such as a microscope or a thermometer, use the highest possible precision. For example, if you're using a microscope to measure the size of a cell, use the smallest possible unit of measurement.

  • Check your work: Once you've calculated the percent error, check your work. Make sure that your answer is logical and that you have made no mistakes in your calculations.


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