Degrees to Radians Calculator

How to Convert Degrees to Radians?

To convert degrees to radians, use the conversion formula. Since π radians equals 180°, you can convert degrees to radians with the following formula:

Radians = degrees × π / 180

In other words, the angle in radians equals the angle in degrees multiplied by π, then divided by 180.

Conversion Example

Convert 45 degrees to radians:

1. Radians = 45° × π/180
2. Radians = 1 × π/4
3. Radians = π/4 ≈ 0.7854

What Is a Radian?

A radian is a unit of angle measure equal to the length of an arc divided by the radius of the circle or arc. One radian equals 180/π degrees, approximately 57.29578°. There are about 6.28318 radians (2π) in a full circle.

• The radian is the SI derived unit of angle in the metric system and can be abbreviated as rad, or sometimes c, r, or R. For example, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R.
• The angle formula in radians is θ = s/r, where the angle θ in radians equals the arc length s divided by the radius r.
• The radian is also considered a "unitless" unit. When radians are multiplied or divided by radians, the final unit of the result does not include the radian.

Common Degree-Radian Conversion Table

• 0° = 0 radians
• 30° ≈ 0.5236 = π/6
• 45° ≈ 0.7854 = π/4
• 60° ≈ 1.0472 = π/3
• 90° ≈ 1.5708 = π/2
• 180° ≈ 3.1416 = π
• 270° ≈ 4.7124 = 3π/2
• 360° ≈ 6.2832 = 2π