Radians to Degrees Calculator

How to Convert Radians to Degrees?

To convert radians to degrees, use the conversion formula. Since π radians equals 180°, the following formula is preferred in math for its accuracy and convenience:

Degrees = radians × (180 / π)

where π ≈ 3.141592653589793. In other words, degrees equals radians multiplied by 180 divided by π.

Conversion Example

Convert 5 radians to degrees:

1. Degrees = 5 radians × 180/π
2. Degrees = 900/π ≈ 286.48°

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 Radian-Degree Conversion Table

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