Degree and Radian Measure Formula

In mathematics, the radian is the standard unit of angular measure. An angle’s measurement in radians is numerically equal to the length of a corresponding arc of a unit circle. The relationship or the connection between the arc length and radius of a circle defines radian of a circle. Degree and radian formula used to convert, degree to radian or radian to degree.

\[\LARGE Radian=\frac{Arc\;Length}{Radius\;Length}\]

\[\LARGE Radian=\frac{Degree\times \pi}{180}\]

Here are few Degree Measures and their corresponding Radian Measures – 

$\large 30° = \frac{\pi }{6}$

$\large 45° = \frac{\pi }{4}$

$\large 60° = \frac{\pi }{3}$

$\large 90° = \frac{\pi }{2}$

$\large 120° = \frac{2\pi }{3}$

$\large 135° = \frac{3\pi }{4}$

$\large 150° = \frac{5\pi }{6}$

$\large 180° = \pi$

$\large 210° = \frac{7\pi }{6}$

$\large 225° = \frac{5\pi }{4}$

$\large 240° = \frac{4\pi }{3}$

$\large 270° = \frac{3\pi }{2}$

$\large 300° = \frac{5\pi }{3}$

$\large 315° = \frac{7\pi }{4}$

$\large 330° = \frac{11\pi }{6}$

$\large 360° = 2\pi $

Solved Examples

Question 1:

Convert 220° into radian measure?

Solution:

Given Degree = 220°

Formula is,

Radian =  $\frac{degree \times \pi}{180}$

Radian = $\frac{220 \times \pi}{180}$

Radian = $\frac{11 \times \pi}{9}$

Radian = $3.837$


Practise This Question

If the cost of a book worth Rs. 50 is increased by Rs. 25, the rate of increase is