# How do we calculate percentage error?

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Last Updated: January 23, 2020

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The percentage error is, formally, the magnitude of the difference between an exact and an approximate value divided by the magnitude of the exact value per 100 cases (percentage form). Essentially, this allows you to see how far off an approximate value and an exact value are in a percentage of the exact value. The error can be because of measuring errors (tools or human error) or because of approximations used in calculating (rounding errors, for example). Regardless, the formula is straight forward and simple to calculate.

## Steps

### Part 1Part 1 of 2:Calculating the Values Part of the Equation

1**Write down the formula for percentage error.** The formula for calculating percentage error is simple: **[(|Approximate Value - Exact Value|) / Exact Value] x 100**. You will use this as a reference to plug in the two values you need to know.[1] X Research source Go to source

- The approximate value is your estimated value, and the exact value is the real value.
- For example, if you guess that there will be 9 oranges in a bag, but there are actually 10, 9 is the approximate value, and 10 is your exact value.

2**Subtract the exact value from the approximate one.** In the example of oranges, you will subtract 10 (the exact value) from 9 (the estimated value). In this case, the result is 9 - 10 = **-1**. [2] X Research source Go to source

- This difference is considered the magnitude of difference in approximate and estimated values. This begins to tell you how far off the results were from what they were expected to be.

3**Find the absolute value of the top result.** Since the formula uses the absolute value of the difference, you can discard a negative sign. In this example, -1 will become just 1.[3] X Research source Go to source

- In the oranges example, 9 - 10 = -1. The absolute value of -1, written as |-1|, is 1.
- If your result is positive, leave the number as it is. For example, 12 apples (approximate) - 10 apples (exact) = 2. The absolute value of 2 (|2|) is just 2.
- In statistics, taking the absolute value simply means you don't care which direction your guess was off (either too highpositiveor too lownegative). You just want to know how far off the estimate was from the exact value.

4**Divide that result by the absolute exact value.** Either with a calculator or by hand, divide the top number by the absolute value of your exact variable. In this example, the exact value is already positive, so you just need to divide 1 (from the previous step) by 10 (the exact number of oranges).[4] X Research source Go to source

- For this example, 1/|10| = 1/10.
- In some cases, the exact value might be a negative number to begin with. If this is the case, you want to ignore the negative (i.e. take the absolute value of the exact number).[5] X Research source Go to source

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### Part 2Part 2 of 2:Finalizing Your Answer in Percentage Form

1**Convert the fraction**** into decimal form.** To convert the fraction into a percentage, it is easiest to have a decimal number. For our example, 1/10 = 0.1. Calculators will be able to convert more difficult numbers quickly for you.

- If you cannot use a calculator, it may take using long division to convert the fraction to a decimal. Usually, about 4 or 5 digits past the decimal place will be sufficient to round to.
- You should always be dividing a
**positive**number by a**positive**number when converting to decimal form.

2**Multiply**** the result times 100.** Simply multiply the result, 0.1 in this example, by 100. This will convert the answer into percentage form. Just add the percentage symbol to the answer, and you're done.[6] X Research source Go to source

- In this example, 0.1 x 100 = 10. Add the percent sign to get 10%, your percentage error.

3**Check your work to make sure the answer is correct.** Often swapping signs (positive/negative) and dividing can lead to minor errors in your calculations. It is best to go back to check your answer makes sense.

- In our example, we want to make sure that our approximation of 9 oranges is off by 10% of the actual value of oranges. 10% (10% = 0.1) of 10 oranges is 1 (0.1 x 10 = 1).
- 9 oranges +
**1**= 10 oranges. This confirms that the guess of 9 was indeed off by just 1 oranges or 10% of the actual value of 10 oranges.

## Community Q&A

- Question In a resistor, the relationship between the voltage V, the current I and resistance R, is given by Ohm's law: V=IR. If the voltage is constant, how is the relative change in R related to the relative change in the current?

Donagan Top Answerer I and R are inversely proportional. That means that as I increases, R decreases by the same percentage (and vice versa).

- Question Do I use significant figures while calculating percentage error?

Donagan Top Answerer Yes.

- Question How do I calculate the percentage error in the kinetic energy of a particle?

Community Answer Multiplying the relative errors of measuring the mass and the velocities should do.

- Question How do I find the percentage error when the numerator is going to be a negative?

Donagan Top Answerer The sign of the numerator doesn't matter. It has no effect on the percentage.

- Question What happens if my exact value is less then my theoretical value? Is there such thing as a negative percent error?

Community Answer If it is less than the true value, the percent error will be negative. If it is greater than the true value, the percent error will be positive.

- Question How do I calculate a percentage error when resistors are connected in a series?

Community Answer Carry the 2 and get the square root of the previous answer.

- Question How do I find the percent error in an experiment with three trials?

Community Answer Find the average percentage of your three trials. You can do this by finding the percent of each trial, adding them all together, and then dividing it by the number of trials (which, in this case, is 3). Use that average in your calculation to find the percent error.

- Question How do I calculate percentages?

Community Answer Divide the amount you have by the total amount possible, then multiply by 100. E.g. If you have 5 apples and there are 20 apples altogether, then you have 5/20=0.25*100=25% of the apples.

- Question A number, 5.7810101, is wrongly written as 5.9810101. What is the percentage of error?

Donagan Top Answerer The error is 5.981 - 5.781 = 0.2. 0.2 / 5.781 = 0.034596, so the percentage of error is 3.4596%.

- Question How do I calculate the percentage error when more than one result is obtained?

Community Answer You can choose to sum up the results, or do the results separately, then count the average of the error percentage. See more answers

## Video

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## Tips

- You may see the values called experimental (approximate) and theoretical (exact). Make sure to use the value you are comparing against as the exact value.
- Oddly enough, since you will take the absolute value of the difference in approximate and exact values, it doesn't matter which order you subtract the values. For example, |8 - 4| = 4 and |4 - 8| = |-4| = 4. The values turn out to be the same!

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## References

- http://www.mathsisfun.com/numbers/percentage-error.html
- https://www.mathsisfun.com/numbers/percentage-error.html
- https://www.mathsisfun.com/numbers/percentage-error.html
- https://www.mathsisfun.com/numbers/percentage-error.html
- http://astro.physics.uiowa.edu/ITU/glossary/percent-error-formula/
- https://www.mathsisfun.com/numbers/percentage-error.html

## About This Article

Co-authored by: wikiHow Staff wikiHow Staff Writer This article was co-authored by wikiHow Staff. Our trained team of editors and researchers validate articles for accuracy and comprehensiveness. wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article is backed by trusted research and meets our high quality standards. This article has been viewed 584,514 times. Co-authors: 18 Updated: January 23, 2020 Views:584,514 Article Rating:72% - 88 votes Categories: Probability and Statistics Article SummaryX

To calculate percentage error, use the formula: [(exact value - approximate value)/exact value] x 100. First, subtract the approximate value from the exact value. Then, divide that number by the exact value. Finally, convert fractions to decimal form and multiply your answer by 100 to find the percentage error. If you want to learn how to check your answers, keep reading the article!In other languagesItaliano:Calcolare la Percentuale d'Errore Português:Calcular o Erro Relativo Percentual Deutsch:Die prozentuale Abweichung berechnen Español:calcular el porcentaje de error Français:calculer un pourcentage d'erreur 中文:计算误差百分比 Русский:вычислить процентную погрешность Bahasa Indonesia:Menghitung Galat Persentase Nederlands:Een foutpercentage berekenen ไทย:หาค่าคลาดเคลื่อนร้อยละ العربية:حساب النسبة المئوية للخطأ 日本語:百分率誤差を計算する Tiếng Việt:Tính phần trăm sai số 한국어:백분율 오차 계산하는 법

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## Reader Success Stories

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Apr 11, 2019 "I was confused on how to deal with negative numbers when calculating percentage error, but now I know I can just use the absolute value." Rated this article:

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