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By Shailendra Singh
|
Updated on 5 Mar 2025, 15:02 IST
Radians and degrees are units used to measure angles. Degrees are the more common unit, where a circle is divided into 360 equal parts. Radians are an alternative unit based on the radius of a circle, with 2π radians in a full circle. They’re used in mathematics, physics, and engineering to describe rotations and angles.
To convert radians to degrees, you can use the following formula:
Degrees = Radians × (180 / π)
Where:
Example – Convert 6 radian to degree
Ans. Degrees = 6 × (180 / π)
= 6 x (180 / 3.14159)
= 6 x 57.295
= 343.77
| Radians (rad) | Radians (rad) | Degrees (°) |
| 0 rad | 0 rad | 0° |
| π/6 rad | 0.5235987756 rad | 30° |
| π/4 rad | 0.7853981634 rad | 45° |
| π/3 rad | 1.0471975512 rad | 60° |
| π/2 rad | 1.5707963268 rad | 90° |
| 2π/3 rad | 2.0943951024 rad | 120° |
| 3π/4 rad | 2.3561944902 rad | 135° |
| 5π/6 rad | 2.6179938780 rad | 150° |
| π rad | 3.1415926536 rad | 180° |
| 3π/2 rad | 4.7123889804 rad | 270° |
| 2π rad | 6.2831853072 rad | 360° |
To convert radians to degrees, you can use the following formula: Degrees = Radians × (180/π). Multiply the radians value by 180 and divide by π (approximately 3.14159) to get the equivalent value in degrees.
The degree measure of π (pi) in radians is 180 degrees. This means that one full circle, which is 360 degrees, corresponds to 2π radians.
The formula for converting 1 radian to degrees is: Degrees = 1 radian × (180/π), which simplifies to approximately 57.2958 degrees.
The value of 2π/3 radians in degrees is approximately 120 degrees.
The value of 2π/8 radians in degrees is 45 degrees. This simplifies to 1/8 of a full circle.
The value of 3π/4 radians in degrees is approximately 135 degrees. This corresponds to three-fourths of a full circle.
The value of 7π/4 radians in degrees is approximately 315 degrees. This is more than a full circle (2π radians) by 1/4 of a circle.
The value of 15π/4 radians in degrees is 135 degrees. This is because 15π/4 radians is equivalent to three and three-fourths of a full circle.