Free Angle Converter
Convert between degrees, radians, gradians, arcminutes, arcseconds, and turns. Instant angle unit conversion for math, engineering, and navigation.
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180 Degrees =
Formula
Degrees to Radians: rad = deg × π/180 | Radians to Degrees: deg = rad × 180/π | 1 turn = 360°How to Convert Angle Units
Angle conversion normalizes all values to degrees, then converts to your target unit. While degrees are the most familiar, radians are essential in mathematics and physics, and arcminutes/arcseconds are used in astronomy and navigation.
Angle Units Explained
- Degrees (°) — the most common angle unit. A full circle is 360°. Used in everyday life, construction, and navigation.
- Radians (rad) — the SI unit of angle. A full circle is 2π radians. Essential in trigonometry, calculus, and physics.
- Gradians (gon) — a full circle is 400 gradians. A right angle is exactly 100 gradians. Used in surveying.
- Arcminutes (') — 1/60 of a degree. Used in astronomy and geographic coordinates.
- Arcseconds (") — 1/3600 of a degree. Used for precise astronomical measurements.
- Turns — one complete rotation = 1 turn = 360° = 2π radians.
Key Angle References
- Right angle: 90° = π/2 rad = 100 gon
- Straight angle: 180° = π rad = 200 gon
- Full rotation: 360° = 2π rad = 400 gon = 1 turn
- 1 radian: ≈ 57.296°
- Common triangle angles: 30°, 45°, 60°, 90°
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by π/180 (approximately 0.01745). For example, 180° × π/180 = π radians ≈ 3.14159. Common values: 90° = π/2, 180° = π, 360° = 2π.
What are gradians used for?
Gradians (also called gons) divide a right angle into 100 units instead of 90, making a full circle 400 gradians. They're used in surveying and some European engineering. 1 gradian = 0.9 degrees.
What is an arcminute and arcsecond?
An arcminute is 1/60 of a degree, and an arcsecond is 1/60 of an arcminute (1/3600 of a degree). They're used in astronomy, navigation, and geographic coordinates. Human eye resolution is about 1 arcminute.
What is a turn?
A turn (or revolution) is one complete rotation — 360 degrees or 2π radians. It's used in physics for rotational motion and in everyday language ('half turn' = 180°).
Why do mathematicians prefer radians?
Radians simplify calculus formulas. The derivative of sin(x) is cos(x) only when x is in radians. A radian is the angle where the arc length equals the radius — a natural geometric relationship.