Table of Contents
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.
How to convert radians to degrees
To convert radians to degrees, you can use the following formula:
Degrees = Radians × (180 / π)
Where:
- Degrees is the angle in degrees.
- Radians is the angle in radians.
- π (pi) is a mathematical constant approximately equal to 3.14159.
Example – Convert 6 radian to degree
Ans. Degrees = 6 × (180 / π)
= 6 x (180 / 3.14159)
= 6 x 57.295
= 343.77
Radians to degrees conversion table
| 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° |
FAQs on Radians to Degrees conversion
How do you convert radians to degrees?
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.
What is the degree measure of π in radians?
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.
What is the formula for converting 1 radian to degrees?
The formula for converting 1 radian to degrees is: Degrees = 1 radian × (180/π), which simplifies to approximately 57.2958 degrees.
What is 2π/3 in degrees?
The value of 2π/3 radians in degrees is approximately 120 degrees.
What is 2π/8 in degrees?
The value of 2π/8 radians in degrees is 45 degrees. This simplifies to 1/8 of a full circle.
What is 3π/4 radians in degrees?
The value of 3π/4 radians in degrees is approximately 135 degrees. This corresponds to three-fourths of a full circle.
What is 7π/4 radians in degrees?
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.
What is 15π/4 radians in degrees?
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.
