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Percent Error Formula

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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 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.

Percent Error Definition

Percent Error is the difference between the actual value and the measured value in any measurement that is calculated in percentage. 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 measured value divide by the estimated value multiplied by the 100.

We can also say that percent error is relative error multiplied by 100.

Percent Error Formula

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 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 example added below,

Percent Error Example

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

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 percent 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 percent error in the calculation.

Read More,

FAQs on Percent Error

1. What is Percent Error?

Percent Error is the difference between the measured value and the actual value expressed as percentage. Percentage error is also calculate by multiplying the relative error by 100.

2. What is Percent Error Formula?

The percent error formula is,

% Error = {|A – E|/A}×100

where,

  • A is Actual Value
  • E is Estimated Value

3. What is the Use of Percent Error Formula?

Various uses of Percent Error Formula is,

  • It is used for Expermimental Measurement.
  • It is used for Quality Contral and Manufactiring.
  • It is used for Caliberation of various instruments.

4. How is Percent Error Calculated?

Percent Error is calculated by the formula (|Measured Value-Actual Value| / Actual Value) x 100



Last Updated : 06 Sep, 2023
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