Percent Error

Percent Error is the percentage difference between the actual value and the measured value in any measurement. Percent Error is very useful because in all the measuring and manufacturing processes there is a possibility of slight error because of Human Error then the percent error is what tells us how much a measurement differs from the original or estimated value.

In this article, we will learn about, percent error, percent error formula, how to calculate percent error, examples, and others in detail.

What is Percent Error?

Percent error is a measure of the accuracy of a measurement or calculation compared to the true or accepted value. It indicates the difference between the observed or calculated value and the true value, expressed as a percentage of the true value.

Percent Error is the percentage difference between the actual value and the measured value in any measurement .

Suppose we are given the task of measuring an object then the percent error in that process is the difference between the estimated value and the

Note: We can also say that percent error is relative error multiplied by 100. ( Percentage Error = Relative Error × 100)

Formula for Percent Error

Percent Error Formula is the formula that is used to calculate the percentage error in any measurement. The formula for percent error is,

Percent Error = (|Measured Value - Actual Value|/Actual Value) × 100

This can also be written as,

% Error = {|A - E|/A}×100

Where,

• A is Actual Value
• E is Estimated Value

How to Calculate Percent Error?

Percent Error is calculated using the steps added below,

Step 1: Measure the value of the observation.

Step 2: Find the difference between the measured value and the estimated/actual value.

Step 3: Find the relative error by taking the ratio of difference and the actual value.

Step 4: Multiply the relative number by 100 to get the percent error.

This can be explained by the examples added below,

Examples Problems on Percent Error

Example 1: The actual length of a straight line is 8cm and when we measured with a scale it was 7cm (Wrong value) due to some marginal error. What is the percentage error?

Solution:

Given,

• Measured value = 7 cm
• Actual Value = 8 cm

Percent Error(PE) = (|Measured Value-Actual Value| / Actual Value) x 100

⇒ PE = (|7-8| / 8) x 100

⇒ PE = (|-1| / 8) x 100

⇒ PE = (1/8) x 100

⇒ PE = 12.5%

So, Percent Error is 12.5%

Example 2: What is the percentage error if the measured value is 40cm and the Actual value is 50cm?

Solution:

Given,

• Measured Value = 40 cm
• Actual Value = 50 cm

Percent Error = (|Measured Value-Actual Value| / Actual Value) x 100

⇒ PE = (|40-50| / 50) x 100

⇒ PE = (|-10| / 50) x 100

⇒ PE = (10/50) x 100

⇒ PE = 20%

So, Percent Error is 20%

Example 3: A scale measures wrongly a value as 15 cm due to some marginal errors. Find the percentage error if the actual measurement of the value is 14 cm.

Solution:

Given,

• Measured Value = 15 cm
• Actual Value = 14 cm

Percent Error(PE) = ( |Measured Value-Actual Value| / Actual Value ) x 100

⇒ PE = ( |15-14| / 14 ) x 100

⇒ PE = ( |1| / 14 ) x 100

⇒ PE = 100/14

⇒ PE = 7.14%

So, Percent Error is 7.14%

Example 4: What is the percentage error if the measured value is 11cm and the Actual value is 10cm?

Solution:

Given,

• Measured Value = 11 cm (Wrongly Measured)
• Actual Value = 10 cm (Exact value)

Percent Error(PE) = ( |Measured Value-Actual Value| / Actual Value ) x 100

⇒ PE = ( |11-10| / 10 ) x 100

⇒ PE = ( |1| / 10 ) x 100

⇒ PE = 100/10

⇒ PE = 10%

So, Percent Error is 10%

Example 5: Find the percentage error if the wrongly measured value is 100 cm and the Actual value is 105 cm?

Solution:

Given,

• Wrongly Measured Value = 100 cm
• Actual Value = 105 cm

Percent Error(PE) = (|Measured Value-Actual Value| / Actual Value) x 100

⇒ PE = (|100-105| / 105) x 100

⇒ PE = (|-5| / 105) x 100

⇒ PE = (5/105) x 100

⇒ PE = 100/21

⇒ PE = 4.76%

So, Percentage Error is 4.76%

Practice Questions on Percent Error Formula

Q1: If the thickness of a rod is 10 mm and the measurement show the thickness to be 10.5 mm. Find the percent error.

Q2: The gravity on Earth is 9.8 m/s². A student peforms the experiment in lab and calculated the gravity to be 9.3 m/s². Find the percentage error in the calculation.

Q3: An accountant calculated the total revenue of a company to be 100 crores while the actual revenue was 110 crore. Find the percentage error in the calculation.

Q4: A scientist estimates the mass of a substance to be 250 grams, but the true mass is 240 grams. Calculate the percent error in the measurement.

Q5: The estimated height of a building is 180 meters, while its actual height is 175 meters. What is the percent error in the estimate?

Q6: A student measures the length of a metal rod as 52 cm, but the actual length is 50 cm. Calculate the percent error.

Q7: The predicted value of a stock price was $120, but the actual value was $115. What is the percent error in the prediction?

Q8: A thermometer reads the temperature as 98°F, but the actual temperature is 100°F. Find the percent error.

Read More,

• Ratio and Proportion
• Compound Interest Formula
• Percentage Change Formula
• Profit Loss Formula
• Percentage Increase Formula
• Percentage Decrease Formula

Conclusion

Percent error is a simple yet powerful tool for evaluating the accuracy of measurements and predictions. It helps quantify how close a measured or estimated value is to the true or accepted value, providing a clear understanding of the margin of error. By using the percent error formula, we can easily assess the reliability of results in various fields, from science experiments to financial forecasts.