Relative Error Formula

Error is the difference between the estimated value and the actual value. The relative error could be calculated in the percent using the relative error formula. Measurement errors arise because of unavoidable faults in the measuring instrument and limitations of the human eye. Errors come in all sizes, and sometimes we need to decide if the error in our measurement is so big that it makes the measurement useless. The smaller the error indicates that we are close to the actual value. Let us study the relative error formula using solved examples in the following sections.

What Is the Relative Error Formula?

Percent error will let us know how much extent these unavoidable errors affect our experimental results. Absolute value can be some times termed as true value or theoretical value. Most of the time, the percentage error is expressed as a positive value. The absolute value of the error  is divided by an accepted value and given as a percent. The formula for finding percent relative error:

Percent Relative Error = \(\left | \dfrac{\text {Actual Value - Estimated Value}}{\text {Actual Value}}\right |\times 100\)

Examples on Relative Error Formula

Example 1: John measured his height and found 5 feet. However, after he carefully measured his height a second time, he found his real height to be 4.5 feet. What is the percent error John made when he measured the first time? Solve it by using the relative error formula.

Solution:     

Before solving the problem, let us identify the information:

Actual value: 4.5 ft and Estimated value: 5 ft

Now,

• Step-1: Subtract one value from others to get the absolute value of error.
  Error = \(\left | 4.5-5 \right |=0.5\)
• Step-2: Divide the error by actual value.
  \(\dfrac{0.5}{4.5}=0.1111  \hspace{1cm} \text {(up to 4 decimal places)}\)
• Step-3: Multiply that answer by 100 and attach % symbol to express the answer as a percentage.
  \(0.111\times 100 = 11.11%\)

Answer: Percentage error = 11.11%

Example 2: Harry got a traffic penalty notice for speeding by police for traveling 70 mph in a 60 mph zone. Harry claimed his speedometer said 60 mph, not 70 mph. What could Harry claim as his percent error? Solve it by using the relative error formula.

Solution:     

Let us arrive at %error in 3 steps:

Absolute Error: \(\left |70 - 60 \right |\) = 10

Relative percent error: 10/60 = 0.1667

0.1667 × 100 =16.67% 

Answer: Harry can claim 16.67% as his percent error.