Angle Converter

Convert between different angle units including degrees, radians, gradians, and more.

From

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°

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

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

• 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)