Percentage Error

CalculatorCrave percentage error calculator is a reliable tool that helps you determine the accuracy of your measurements. Simply input the observed value and the true value, and our calculator will quickly calculate the percentage error for you. This can be helpful in a variety of fields, such as science, engineering, or statistics, where precise measurements are essential.

What Is Percentage Error

Percentage error is a measure of how inaccurate a measurement is, calculated as the difference between the measured value and the true value, divided by the true value, and multiplied by 100 to express it as a percentage.

Percentage error is important because it provides a quick and easy way to gauge the accuracy of a measurement or prediction. It allows us to compare different measurements or predictions in different situations, taking into account the scale of the quantities being measured.

Examples of situations where percentage error is commonly used include:

1. Price changes: When retailers announce discounts or price increases, the percentage error can help consumers understand the magnitude of the change relative to the original price.

2. Population growth: Demographers use percentage error to estimate population growth rates and forecast future population trends. This helps policymakers understand the impact of population changes on resources and services.

3. Scientific experiments: Researchers use percentage error to evaluate the precision and accuracy of their experimental results. It helps them identify any discrepancies between the observed and expected values.

Calculating Percentage Error

To calculate percentage change or percentage error, you can use the following formula:

Percentage error = (|calculated value - accepted value| / accepted value) * 100%

Let's work through a couple of practice problems to demonstrate how to use these formulas:

Problem 1:

Old value = 50
New value = 70

Percentage change = ((70 - 50) / 50) * 100%
Percentage change = (20 / 50) * 100%
Percentage change = 0.4 * 100%
Percentage change = 40%

Therefore, the percentage change from 50 to 70 is 40%.

Problem 2:

Accepted value = 100
Calculated value = 90

Percentage error = (|90 - 100| / 100) * 100%
Percentage error = (10 / 100) * 100%
Percentage error = 0.1 * 100%
Percentage error = 10%

Therefore, the percentage error in the calculated value of 90 compared to the accepted value of 100 is 10%.