# Percentage Error

## Percentage Error

While measuring any physical quantity, it is impossible in principle to find its true value. The difference between the measured and the true values of a physical quantity is called the error of measurement. To determine if a value is accurate compare it to the accepted value. As these values can be anything a concept called percent error has been developed.

What is Percentage Error?

Errors in measurement may also be expressed in terms of percentage. This is similar to relative error except that the error here is converted to a percent value. The percentage error is found by multiplying the relative error by 100%.

It is the absolute value of the difference of the measured value and the actual value divided by the actual value and multiplied by 100.

$$Percentage\,\,Error\,\,=\,\,\frac{Approximate\,Value\,\,-\,\,Exact\,\,Value}{Exact\,\,Value}\times 100$$.

How to find the Percentage Error?

Problem:

A scale measures wrongly a value as 10cm due to some marginal errors. Calculate the percentage error if the actual measurement of the value is 15cm?

Solution:

Given,

Exact value = 15cm,

Approximate value = 10cm,

Percentage Error =?

$$Percentage\,\,Error\,\,=\,\,\frac{Approximate\,Value\,\,-\,\,Exact\,\,Value}{Exact\,\,Value}\times 100=\frac{10-15}{15}\times 100$$.

$$Percentage\,\,Error\,\,=\frac{10-15}{15}\times 100=-33.33%$$.

$$\therefore \,\,Percentage\,\,Error\,\,=-33.33%$$.