Radians to Degrees

Angles can be measured in two units: degrees and radians. In the degree system, a full rotation is divided into 360°, while in radians it is 2π radians.

Key Relationship

• 360^∘ = 2π radians
• 180^∘ = π radians

To convert radians into degrees & degrees into radians

Key values

• 2π radians = 360°
• π radians = 180°
• 1 Radian = 180/π Degrees = 57.296 Degrees

Example: Convert 60 degrees to radians.

Solution:

Given angle is 60 degrees

Angle in Radian = Angle in Degree × (π/180)

= 60 × (π/180)

= π/3

Hence, 60 degrees is equal to π/3 in radian.

Radians to Degrees Calculator

Conversion Table

The table given below shows the values of angles in radians and their respective values in degrees.

Also Check

• Types of angles
• Pair of Angles

Radians to Degrees Examples

Example 1: Convert 9π/5 radians to degrees.

Solution:

Since, π radians = 180° or 1 radian = 1c = (180/π)°

Hence, (9π/5)^c = (9π/5 × 180/π)° = 324°

Thus, (9π/5)^c = 324^o

Example 2: Convert −5π/6 radians into degrees.

Solution:

We know that π radians = 180° or 1 radian = 1c = (180/π)°

Hence, (−5π/6)^c = (−5π/6 × 180/π)° = −150°

Thus, (9π/5)^c = −150°

Example 3: Convert 18π/5 into degrees.

Solution:

We know that π radians = 180° or 1 radian = 1c = (180/π)°

Hence, (18π/5)^c = (18π/5 × 180/π)° = 648°

Thus, (18π/5)^c = 648°

Example 4: Convert −3 radians into degrees.

Solution:

We know that π radians = 180° or 1 radian = 1c = (180/π)°

Hence, (−3)^c = (−3 × 180/π)° = (180 × 7 × −3/22)° = (−1719/11) = −171°(9 × 60/11)' = −171°49'5''

Thus, (−3)^c = −171^o49'5''

Example 5: Convert 11 radians into degrees.

Solution:

We know that π radians = 180° or 1 radian = 1^c = (180/π)°

Hence, (11)^c = (11 × 180/π)° = (11 × 180 × 7/22) = 630°

Thus, (11)^c = 630°

Example 6: Convert 1 radian to degrees.

Solution:

We know that π radians = 180° or 1 radian = 1^c = (180/π)°

Hence, (1)^c = (1 × 180/π)° = (180 × 7/22) = 57°(3 × 60/11) = 57°16'(4 × 60/11)'' = 57°16'21''

Thus, (1)^c = 57^o16'21''