Angle Converter

Convert between degrees, radians, gradians, and more

From:

ℹ️

To:

ℹ️

Conversion Formula:

Multiply by 0.01745329

Common Conversions

Common Angle Reference

Degrees	Radians	Turns	Gradians
30	π/6 (approx 0.5236 rad)	1/12	33.33 grad
45	π/4 (approx 0.7854 rad)	1/8	50 grad
60	π/3 (approx 1.0472 rad)	1/6	66.67 grad
90	π/2 (approx 1.5708 rad)	1/4	100 grad
180	π (approx 3.1416 rad)	1/2	200 grad
360	2π (approx 6.2832 rad)	1	400 grad

Special Angles and Applications

30 Angle

One hour on an analog clock
Standard roof pitch (30 slope)
Interior angle of a regular dodecagon (12-sided polygon)

45 Angle

Diagonal of a square relative to its sides
Standard miter cut for a perfect corner joint
Common slope in topographic maps

60 Angle

Interior angle of an equilateral triangle
Angle between adjacent hexagon sides
Standard angle in technical drawing

90 Angle

Right angle (perpendicular lines)
Corner of a square or rectangle
Standard orientation in Cartesian coordinates

180 Angle

Straight line (opposite directions)
Reflection operation in geometry
Interior angle of a triangle with parallel sides

360 Angle

Full circle/complete rotation
One cycle in periodic motion
Standard polar coordinate system

Fields That Use Angular Measurement

Navigation & Surveying

Uses degrees, minutes, and seconds for precision positioning and bearing measurements. GPS systems, compasses, and theodolites depend on angular measurements.

Physics & Engineering

Uses radians for calculus, wave mechanics, and rotational dynamics. Crucial for mechanical design, electronics, and structural analysis.

Astronomy

Uses degrees, arcminutes, and arcseconds for measuring celestial positions and angular diameters. Critical for telescope pointing and orbital mechanics.

About Angle Units

Different angle units are used in various fields:

*
Degrees: Common in everyday use, navigation, and engineering. A full circle is 360.
*
Radians (rad): Standard in mathematics, physics, and calculus. A full circle is 2π radians.
*
Gradians (grad): Used in surveying and some European countries. A full circle is 400 gradians.
*
Arc Minutes and Arc Seconds: Used in astronomy and precise measurements. 1 degree = 60 arcminutes, 1 arcminute = 60 arcseconds.
*
Turns: Used to measure complete rotations. 1 turn = 360 degrees.
*
NATO Mils: Used in military applications. A full circle is 6400 mils.

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Visual Comparison

Angle Visualization

Right angle -90.0° in standard position

Real-world Examples

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Right angle

Corner of a square or rectangle

Field: Construction • 90°

Common Angular Measures

Navigation

360°:Compass rose - Full circle divided into cardinal directions
45°:Intercardinal directions - NE, SE, SW, NW on a compass
1°:Angular minute - 1/60th of a degree in navigation

Architecture

90°:Square corners - Standard wall intersections
30°-45°:Roof pitch - Common angles for roof slopes
120°:Hexagonal layouts - Used in modern architecture designs

Astronomy

23.4°:Earth's axial tilt - Tilt responsible for seasons
360°:Orbital period - Complete revolution around a central body
0.5°:Angular diameter - Apparent size of the moon and sun

Optics

42°:Critical angle (water) - Total internal reflection threshold
49°-56°:Brewster's angle - Polarization angle for materials
180°:Backscatter - Light reflected directly back to source

Mobile tip: Swipe left or right on the unit dropdown to quickly change units, or use the arrow buttons

About the Angle Converter

Convert between degrees, radians, gradians, and more All conversions run instantly in your browser and nothing you enter is sent to a server.

Common Conversion Formulas

From	To	Formula
Degrees (°)	Radians (rad)	rad = ° × (π/180)
Radians (rad)	Degrees (°)	° = rad × (180/π)
Degrees (°)	Gradians (grad)	grad = ° × (10/9)