Percentage Error - Formula, Calculation and Examples

Percentage Error

Percentage error is a way to measure how far a measured or estimated value is from the true or actual value. It tells you how accurate your measurement or guess is by expressing the difference as a percentage.

For example, if you estimated that your textbook weighs 1.5 kg but its actual weight is 1.6 kg, the percentage error tells you how far your estimate was from the real value.

Percent Error Definition

The percent error definition explains that it is the difference between a measured or estimated value and the actual or true value. This difference is divided by the actual value and then multiplied by 100 to express the result as a percentage.

Read more: Percentage: Meaning, Formulas, and Solved Examples

Percent Error Formula

To calculate the percent error, we use a specific formula:

Percent Error = (∣Measured Value − Actual Value∣Actual Value) × 100 

Let’s break it down:

• Measured Value: The number you observed or guessed

• Actual Value: The correct or accepted number

• |...|: The absolute value, which makes sure the error is always positive

Using this percent error formula, you can calculate how close or far off your result is.

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Why is Percent Error Important?

Percent error plays a key role in understanding how accurate a result is. It is useful in many areas like math, science and business. Here are some reasons why percent error is important

• It shows how close your measurement or prediction is to the actual value

• It helps you spot mistakes or issues in your method or experiment

• It allows you to evaluate the quality of your results

• It teaches you how to improve accuracy in future measurements

• It helps you better understand and analyze the results of your work

Understanding percent error can make your experiments more reliable and your answers more meaningful.

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Percent Error Calculator

Sometimes you may want to calculate the percent error quickly without doing the math manually. That’s where a percent error calculator is useful.

A percent error calculator takes your measured and actual values and gives you the result instantly. You just input the two values, and it applies the percent error formula behind the scene.

Also read: Discounts: Definition, Formula, Rate

Percent Error and Percentage Difference

Many students confuse percent error with percentage difference, but they are not the same. Each one is used in different situations, and understanding how they work can help you solve problems more accurately.

Percent error is used when you compare a measured or estimated value to a known or actual value. It tells you how far off your measurement is from the correct value.

Example: You estimate the height of a book to be 28 cm. The actual height is 30 cm.
The percent error is

(∣28 − 30∣/30) ×100 = (2/30)×100 = 6.67%

This means your estimate was 6.67 percent lower than the actual value.

Percentage difference is used when comparing two measured values, and there is no exact or correct value to start with. It shows how different the two values are from each other.

Example: Two students measured the same stick. One got 42 cm and the other got 45 cm. The percentage difference is

(∣42 − 45∣ / 42 + 45/2) × 100 = (3/43.5) × 100 = 6.90%

This tells us the two measurements differ by 6.90 percent from each other.

Knowing the difference between percent error and percentage difference helps you choose the right method and avoid mistakes in math and science problems.

Also read: Perimeter of Square - Formula, Definition, Examples

Examples On Percent Error Formula

Example 1: A mechanic measures the radius of a metal nut as 0.5 inches while assembling a machine. However, the actual known radius of the nut is 0.47 inches. Using the percent error formula, calculate the percent error in the measurement.

Solution
Measured value = 0.5 inches

Actual value = 0.47 inches

First, find the difference between the two values:

|0.5 − 0.47| = 0.03

Now divide the difference by the actual value:

0.03 ÷ 0.47 = 0.0638

Multiply the result by 100 to convert it to a percentage:

 0.0638 × 100 = 6.38 percent

The percent error in the measurement is 6.38 percent.

Example 2: While weighing fruit at a market, a student estimates the weight of a mango to be 1.2 kilograms. Later, it is found that the actual weight of the mango is 1.4 kilograms. What is the percent error in the student’s estimation?

Solution
Measured value = 1.2 kilograms

Actual value = 1.4 kilograms

|1.2 − 1.4| = 0.2

0.2 ÷ 1.4 = 0.1429

0.1429 × 100 = 14.29 percent

The percent error in the estimation is 14.29 percent

Example 3: During a science experiment, a student records the volume of liquid in a container as 750 milliliters. After checking with a calibrated measuring tool, the actual volume is found to be 725 milliliters. Find the percent error in the student’s measurement.

Solution
Measured value = 750 milliliters

Actual value = 725 milliliters

|750 − 725| = 25

25 ÷ 725 = 0.0345

 0.0345 × 100 = 3.45 percent

The percent error in the measurement is 3.45 percent

Example 4: A student guesses that the length of a classroom desk is 120 centimeters. When measured accurately with a measuring tape, the actual length is found to be 125 centimeters. What is the percent error in the student’s guess?

Solution

Measured value = 120 centimeters

Actual value = 125 centimeters

|120 − 125| = 5

5 ÷ 125 = 0.04

0.04 × 100 = 4 percent

The percent error in the guess is 4 percent

Example 5: A digital scale shows a person’s weight as 98.5 kilograms, but a more accurate medical scale shows the actual weight to be 100 kilograms. Using the percent error formula, calculate the percent error in the digital scale's reading.

Solution
Measured value = 98.5 kilograms

Actual value = 100 kilograms

|98.5 − 100| = 1.5

1.5 ÷ 100 = 0.015

0.015 × 100 = 1.5 percent

The percent error in the scale reading is 1.5 percent.

Also read: Straight Angle - Meaning, Properties, Examples

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