Degrees to Radians
One degree equals 0.017453 radians.
Radians = degrees ÷ 57.2957795131
Angle Conversion
Common Angles
Angle Reference Guide
Angle Unit Relationships
1 full circle = 360° = 2π rad = 400 gon
1 degree (°) = π/180 rad ≈ 0.01745 rad
1 radian (rad) = 180°/π ≈ 57.296°
1 gradian (gon) = 0.9° = π/200 rad
1 turn = 360° = 2π rad = 400 gon
1 arc minute (') = 1/60° ≈ 0.01667°
1 arc second (") = 1/3600° ≈ 0.000278°
1 milliradian = 0.001 rad ≈ 0.05729°
Common Angle Values
30° = π/6 rad ≈ 0.524 rad
45° = π/4 rad ≈ 0.785 rad
60° = π/3 rad ≈ 1.047 rad
90° = π/2 rad ≈ 1.571 rad
120° = 2π/3 rad ≈ 2.094 rad
180° = π rad ≈ 3.142 rad
270° = 3π/2 rad ≈ 4.712 rad
360° = 2π rad ≈ 6.283 rad
Applications & Usage
Degrees: Most common, navigation, everyday use
Radians: Mathematics, physics, engineering
Gradians: Surveying, some European countries
Arc minutes/seconds: Astronomy, precise measurements
Milliradians: Military, ballistics, optics
Turns: Computer graphics, rotational mechanics
Trigonometric Relationships
• Radians are the "natural" unit for trigonometric functions
• π radians = 180° (half circle)
• 2π radians = 360° (full circle)
• Arc length = radius × angle (in radians)
• 1 radian ≈ 57.3° (the angle that creates an arc equal to the radius)
Degrees to Radians Conversion Table
| ° | rad |
|---|---|
| 1 | 0.0175 |
| 5 | 0.0873 |
| 10 | 0.1745 |
| 15 | 0.2618 |
| 30 | 0.5236 |
| 45 | 0.7854 |
| 60 | 1.0472 |
| 75 | 1.309 |
| 90 | 1.5708 |
| 120 | 2.0944 |
| 135 | 2.3562 |
| 150 | 2.618 |
| 180 | 3.1416 |
| 270 | 4.7124 |
| 360 | 6.2832 |
About This Conversion
Degrees to radians multiplies by π/180, about 0.0174533. Radians are the natural unit for angles because they measure arc length in radii: an angle of one radian cuts an arc exactly as long as the radius, which is what makes the calculus of sine and cosine come out clean.
Every programming language trigonometric function expects radians, so this conversion is the most common source of silent errors in graphics and geometry code. Passing 90 to a sine function returns 0.894, not 1, because it read the input as 90 radians, roughly fourteen full turns.
Frequently Asked Questions
How many radians is 90 degrees?
90° is π/2 radians, about 1.5708.
How many radians is 180 degrees?
180° is exactly π radians, about 3.14159.
What is the formula?
Multiply degrees by π/180, which is about 0.0174533.
Why do programming languages use radians?
The trigonometric identities and derivatives only hold in radians, so the standard libraries define their functions that way.
Related Conversions
Converting the other way? Radians to Degrees
Need a different unit? Open the full angle converter