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Percent Error: Formula, Definition, And Solved Example

Percent errors represent the magnitude of our measurement errors during the analysis procedure. Smaller percent errors imply proximity to the accepted or original value. For instance, an error of 1% suggests that we were close to the accepted value, but an error of 48% shows that we were fairly far from the actual value. Due to factors such as trembling hands, imprecise materials, or the inability of our measurement instruments to estimate precisely, measurement errors are frequently unavoidable. The percent error formula will reveal how these inevitable errors have affected our results.

Percent Error Definition

The percentage error is the difference between the estimated and actual values, expressed as percentages. In other words, the percent error equals 100 times the relative error.

Percent Error Formula

The Percent error formula is:

PE = (|Estimated Value-Actual value|/ Actual value) × 100

Or

Percent Error

Here,

T = True And/or Actual value

E = Estimated value

How Is The Percent Error Calculated?

Detailed instructions for calculating the percent error are provided below.

1 – Calculate the difference between one value and another. If we ignore the sign, the sequence is irrelevant. However, we must subtract the original value from the calculated value if we maintain negative signs. This is an “error” value.

2 – Divide the error by its correct or ideal value (not estimated or measured). This results in a decimal number.

3 – Multiply the decimal number by 100 to transform it into a percentage.

4 – Add a percentage sign (%) to denote the percent error value.

Percent Error Of Mean

What does percent error mean, or Mean percentage error is the average of all the model’s percent errors? This is the formula for the mean percentage error:

Percent Error

Here,

Ti = True And/or actual value of the ith quantity

Ei = Estimated value of the ith quantity

n = The Number of quantities in the model

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This measure’s primary drawback is that it is undefined whenever a single actual value is zero.

Percent Error Example

The following examples aid comprehension of percent error.

Example #1:

A young man measured that the area of a rectangle plot was 468 cm2. However, the actual plot area has been recorded as 470 cm2. Calculate the measurement’s percent error.

Solution:

Given,

468 cm2 = Measured area value

470 cm2 = Actual area value

Detailed Calculation:

1 – Subtract one value from another: 468 minus 470 is -2

Well, by ignoring the negative sign, the difference is 2, representing an error.

2 – Divide the error by the actual value; 2/470 = 0.0042531

Multiplying this value by 100; 0.0042531 × 100 = 0.42% (expressing it in two decimal points) Therefore, the percent error is 0.42%.

Example #2:

On January 1, a new business was established. He anticipated a specific number of consumers to visit his shop each month based on the need in that area. The following table details the number of customers that visited the shop during the first quarter.

Month Expected number of visitors Number of people visited
January 500 450
February 600 500
March 630 600

Determine the mean percent error for the preceding data.

Solution:

Month Difference (ignoring the sign) Relative error Percent error
January 50 0.1111 0.1111 × 100 = 11.11%
February 100 0.2 0.2 × 100 = 20%
March 30 0.05 0.05 × 100 = 5%

Mean percent error = (11.11% + 20% + 5%)/ 3

= 36.11%/3

=12.0367% (Approx.)

Note: 

The goal of calculating the percent error is to determine how closely the measured value corresponds to the actual value. It is a component of exhaustive error analysis. In most fields, percent error is always expressed as a positive number; however, a positive or negative value is acceptable in others. The sign’s purpose is to determine if recorded values regularly exceed or fall below.

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