Angle Converter
Convert between different angle units including degrees, radians, gradians, and more.
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)
Understanding Angle Conversions
Angle conversions relate degrees, radians and gradians. Degrees (360 in a full circle) are the most familiar, while radians are the natural unit in mathematics and physics because they relate an arc length directly to the radius, a full circle is 2π radians.
The core conversion is that 180 degrees equals π radians, so to go from degrees to radians you multiply by π/180. Gradians (also called gons) divide a circle into 400 units and are used in some surveying contexts, where a right angle is a convenient 100 gradians.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply the degree value by π/180 (about 0.0174533). For example, 90° = π/2 ≈ 1.5708 radians.
How many radians are in a full circle?
A full circle is 2π radians, approximately 6.2832 radians.
What is a gradian?
A gradian (or gon) divides a full circle into 400 units, so a right angle is 100 gradians. It is mainly used in surveying.
How many degrees is 1 radian?
One radian equals approximately 57.2958 degrees.