Instantly convert between all major angle units — degrees, radians, gradians, turns, arcminutes, and arcseconds. Used in mathematics, engineering, astronomy, and navigation. Free and private.
Understanding each angle unit helps you choose the right one for your field — from everyday geometry to professional engineering and astronomy.
The most common unit. A full circle = 360°. Used in everyday geometry, navigation, maps, and most educational contexts worldwide.
The standard unit in mathematics and physics. A full circle = 2π radians. Used in calculus, trigonometry, and all scientific computing.
A right angle = 100 gradians, full circle = 400 gradians. Used in surveying, civil engineering, and some European navigation systems.
One full rotation = 1 turn. Simple and intuitive for describing complete rotations in engineering and animation contexts.
1/60th of a degree. Used in astronomy for stellar coordinates, GPS precision, and geographic coordinates (latitude/longitude).
1/3600th of a degree. Used in high-precision astronomy, geodesy, and telescope positioning where extreme angular precision is required.
Multiply degrees by π ÷ 180. Example: 90° × (π/180) = π/2 ≈ 1.5708 radians.
Multiply radians by 180 ÷ π. Example: π radians × (180/π) = 180 degrees.
Multiply degrees by 10 ÷ 9. Example: 90° × (10/9) = 100 gradians (a right angle).
Multiply the degree value by π/180 (approximately 0.017453). For example: 180° × π/180 = π ≈ 3.14159 radians. For 90°: 90 × π/180 = π/2 ≈ 1.5708 radians.
Multiply the radian value by 180/π (approximately 57.2958). For example: 1 radian × 180/π ≈ 57.296°. For π radians: π × 180/π = 180°.
A gradian (also called gon or grad) divides a right angle into 100 units, making a full circle 400 gradians. It simplifies calculations in surveying and civil engineering because horizontal and vertical are always at 100 gradians, not 90 degrees.
There are 60 arcminutes in one degree and 3,600 arcseconds in one degree. These subdivisions are used in astronomy for star positions, in GPS systems, and in geographic coordinates where latitude and longitude are expressed in degrees, minutes, and seconds.
Radians are the natural unit for angles in mathematics because they directly relate arc length to radius (arc length = radius × angle in radians). This makes calculus formulas for trigonometric functions cleaner — the derivative of sin(x) is cos(x) only when x is in radians.
Key radian values: 0° = 0, 30° = π/6 ≈ 0.5236, 45° = π/4 ≈ 0.7854, 60° = π/3 ≈ 1.0472, 90° = π/2 ≈ 1.5708, 180° = π ≈ 3.1416, 270° = 3π/2 ≈ 4.7124, 360° = 2π ≈ 6.2832.
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