Percent Error Formula

There may be a slight manufacturing error in measuring instruments. They can never be assumed to be exact. To get to know to what extend error is there, we go for this percent error formula.

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.

Percent Error Formula is

\[\large Percentage\;Error=\frac{Approximate\;Value-Exact\;Value}{Exact\;Value}\times 100\]

Solved Examples

Question 1: A scale measures wrongly a value as 8 cm due to some marginal errors. Calculate the percentage error if the actual measurement of the value is 12 cm.


Approximate value = 8 cm
Exact value = 12 cm

Percentage Error = $\frac{Approximate Value – Exact Value}{Exact Value}$ $\times$ 100

$Percentage\;Error=\frac{8-12}{12}\times 100$

= -33.3%

Practise This Question

Observe the pattern given below



Then term at nth position will be given by expression