Percent error in a collection of data is the difference between the exact and approximate values compared to the original value. This percent error is expressed as a percentage and hence multiplied by 100.

You can express percent error as absolute error or relative error. Errors may occur because of precision error in a machine, computing error, measurement error, or environmental conditions. 

Percent errors help us to determine how significant our errors are during any analysis. More minor percent errors mean that we are close to the original value, while more substantial percent errors mean a considerable discrepancy between the actual value and approximate value. 

For example, a 2% error would mean that we are very close to the original value, while a 56% error would mean a massive difference between the actual and approximate value. 

Errors while measuring are pervasive because hands may shake during measurements, instruments may be faulty, material may not be precise, etc. 

Percent error calculation

To calculate percent error, you must have two available values. One is the exact value, and the second one is the approximate value. Subtract both these values and then divide them with the original value. Since percent error is expressed in the form of percent, multiply the number thus received by 100. In other words, percent error is relative error multiplied by 100. 

Percentage Error = [(Actual Value – Expected Value) / Expected Value] × 100

Components of the formula

Actual value: The actual value indicates the numerical value of particular reading. The actual value should have been recorded while taking the reading, but due to some errors, we could not record this value. It is a common value that is ideal for carrying out calculations. 

Expected value: The expected value indicates the reading recorded while experimenting. It is not similar to the actual value in most cases because of error. Errors may be due to default in the machine, error while taking the reading, or environmental factors such as air or broken and damaged instruments. 

Some Examples 

Example 1

A boy was measuring the area of a triangle, and according to him, the reading was 462 sq. cm. However, the original area of the square is 465 sq. cm. Calculate the percent error.

Solution

Value of measured area = 462 sq. cm

Value of actual area = 465 sq. cm

Calculation 

Difference of actual value – measured value: 465-462 = 3

So, 3 is the measurement error.

Divide the error by the actual value – 3/465 = 0.00645

Multiplying the value obtained by 100 – 0.00645 X 100 = 0.64%.

Therefore, the percent error in calculating the area of a triangle is 0.64%

Example 2

Suppose you were planning a party and an estimated 20 people would be attending the party while only 18 people managed to come. Calculate the percent error in your estimation.

Solution

The original number of people expected = 20

People who came = 18

Calculation

Difference of actual value – final value = 20 – 18 = 2

So, 2 is the error over here.

Divide the error by the actual value – 2/20 = 0.1

Multiplying the value by 100 – 0.1 X 100 = 10%

Therefore, the percent error in estimating the number of guests is 10%.

Example 3 

Suppose you performed an experiment to measure the boiling point of water, and while experimenting, you found the results to be 102°C. The actual freezing point of water is 100°C.

Solution

The actual boiling point of water = 100° C

The recorded boiling point of water = 102°C

Calculation

The difference between the actual value and calculated value = 100 -102 = 2°C (Percent error can never be negative, so we keep it positive only).

So, 2 is the error over here.

Divide the error by the actual value – 2/100 = 0.02

Multiplying the value obtained by 100 – 0.02 X 100 = 2%

Therefore, the percent error in measuring the boiling point of water is 2%. 

Real-world scenarios where percent error is important

  • Percent error plays a significant role in helping you to determine whether a particular task you completed was up to the mark or not. It helps you in pointing out your mistakes. 
  • Percent error may be helpful in laboratory procedures and large industries with no scope for the slightest error. 
  • Percent error also finds its usage when we have a bulk order to complete, and there cannot be any scope of error in its completion. 
  • In science laboratories, the use of percentage error is critical.

Percent Error vs. Absolute Error

An absolute error in a measurement is the difference between the actual and calculated values. The unit of fundamental error is the same as the initial value. 

Example

Suppose you were planning to purchase 2 kg mangoes while the shopkeeper measured 1.98 kg for you. The absolute error, in this case, will be 2 – 1.98 = 0.02.

On the other hand, percent error is calculated by dividing absolute error by the original value and then multiplying the answer obtained by 100. Percent error is a unitless quantity.

In the above example, the absolute error is 0.02.

Now to calculate the percent error, we will divide it by 20. 

0.02/20 = 0.001

The percent error, in this case, is thus 0.001 X 100 = 0.1%.

Percent error vs. Relative error

The relative error in any calculation is the absolute error divided by the actual value. This means that percent error is the difference between the true value and the observed value divided by the actual value. 

Example

The weather forecast expected the temperature today to be 38°C. However, it rose to 42°C.

First we find the difference between the two numbers, i.e., the expected value and the actual value.

42° – 38° = 4°C

Now for calculating relative error, we divide this number by the actual number, i.e., 38°C 

4/38 = 0.1052

On the other hand, the percent error is a relative error multiplied by 100.

In the above example, the percent error will be 0.1052 X 100 = 10.52%.

Now, you might find it pretty easy to calculate percent error, relative error, or absolute error.

You can make percent error calculations easier by taking the help of several online percent error calculators. Now, you won’t have to wonder how to calculate percent error because these calculators can do it all for you.

Error calculation tools

#1. Calculator Soup 

The Calculator Soup helps you to calculate the percentage error between the experimental value and the actual value. All you have to do is input the values and wait for the results. The calculator performs all the calculations by itself and gives you accurate results. 

Calculator Soup

The page displays two different columns wherein you input the value of numbers you want to calculate percent error for and let the calculator do the rest of the magic. 

#2. Calculator.net

Calculator.net has two columns where you enter the actual and estimated values and let the calculator do the rest of the calculations. This comes in handy when there are plenty of samples of data you want to calculate, and you don’t have the time to calculate the percent error in every case manually. The calculator eases the process and gives you the answer immediately without much delay. 

Calculator.net

Percent errors are inevitable. You can only lower their value, but there won’t be any incidence when the reading of percent error goes to zero. It can be approximately zero but can never be an exact zero. 

#3. Good Calculators

Many online calculators may help you in solving your percentage error problems. Of these, one of the handiest is the Good Calculators. In this calculator, you just input the estimated and original value, and it will automatically give the results.

It saves you from the hassle of performing extensive calculations and protects your time. You can quickly solve comprehensive calculations within seconds and save you a lot of time. 

percent error calculator

Thus, a calculator is ideal for the calculation of percent error when you have extensive data available at hand but are running short of time.

Conclusion

Errors in calculations can completely ruin any project or research. This is where you can take the help of online percent error calculators to get the work done more efficiently and without any human errors.

If you are into finance, you may look at some of these profit percentage calculators.