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By Shailendra Singh
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Updated on 5 Mar 2025, 15:36 IST
Degrees and radians are two different units of measurement used to quantify angles in geometry and trigonometry.
Degrees are the most common unit for measuring angles. A circle is divided into 360 degrees, and each degree is further divided into minutes (‘) and seconds (“). This system is widely used in everyday contexts, such as measuring angles in maps, navigation, and many day-to-day activities.
Radians are an alternative unit for measuring angles, particularly in mathematical calculations involving trigonometric functions. A radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
In a complete circle, there are 2π radians (approximately 6.283 radians). Radians are often preferred in advanced mathematics and physics because they simplify trigonometric formulas and calculations.
To convert degrees to radians, you can use the following formula:
Radians = Degrees × (π / 180)
Here’s the step-by-step process:
For example, let’s say you want to convert 45 degrees to radians:
Radians = 45 × (π / 180)
Radians = 0.25π
So, 45 degrees is approximately equal to 0.25π radians.
| Degrees (°) | Radians (rad) | Radians (rad) |
| 0° | 0 rad | 0 rad |
| 30° | π/6 rad | 0.5235987756 rad |
| 45° | π/4 rad | 0.7853981634 rad |
| 60° | π/3 rad | 1.0471975512 rad |
| 90° | π/2 rad | 1.5707963268 rad |
| 120° | 2π/3 rad | 2.0943951024 rad |
| 135° | 3π/4 rad | 2.3561944902 rad |
| 150° | 5π/6 rad | 2.6179938780 rad |
| 180° | π rad | 3.1415926536 rad |
| 270° | 3π/2 rad | 4.7123889804 rad |
| 360° | 2π rad | 6.2831853072 rad |
To convert degrees to radians, you can use the formula: radians = degrees × (π / 180), where π (pi) is approximately 3.14159. Multiply the number of degrees by π divided by 180 to obtain the equivalent value in radians.
The formula to convert radians to degrees is: degrees = radians × (180 / π). Multiply the number of radians by 180 divided by π to get the equivalent value in degrees.
The value of 1 degree in radians is approximately 0.01745 radians. This is obtained by dividing π by 180.
To convert degrees and minutes to radians, first convert the minutes to decimal form (divide minutes by 60), then follow the formula: radians = (degrees + decimal_minutes) × (π / 180). For example, to convert 40 degrees 20 minutes, first, convert 20 minutes to (20 / 60) = 0.3333 degrees. Then, calculate radians = (40 + 0.3333) × (π / 180).
To convert 270 degrees to radians, use the formula: radians = degrees × (π / 180). Thus, radians = 270 × (π / 180), resulting in approximately 4.7124 radians.
To convert 180 degrees to radians, apply the formula: radians = degrees × (π / 180). Therefore, radians = 180 × (π / 180), which equals π radians.
Convert 120 degrees to radians using the formula: radians = degrees × (π / 180). Thus, radians = 120 × (π / 180), yielding approximately 2.0944 radians.