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Angle Converter

Convert between degrees, radians, gradians, arcminutes, arcseconds, turns and mils - instantly.

UnitValue
Reference

Key Angle Reference Points

Right Angle

90° = π/2 rad = 100 grad = 5,400 arcmin

Straight Angle

180° = π rad = 200 grad = 0.5 turn

Full Circle

360° = 2π rad = 400 grad = 1 turn

Use Cases

When to Convert Angles

Trigonometry & Maths

Convert degrees to radians for sin/cos/tan calculations in programming (JavaScript uses radians).

Navigation & Surveying

Convert bearing angles between degrees and arcminutes/arcseconds for GPS and maps.

Astronomy

Work with star coordinates in arcminutes and arcseconds when reading sky charts.

Engineering & CAD

Convert angles between degrees and radians for rotation matrices and mechanical design.

Military & Optics

Convert between degrees and mils (NATO) for artillery range calculations.

Solar Panel Positioning

Set solar panel inclination angles - convert between degrees and gradians as needed.

FAQ

Angle Conversion Questions

Radians = Degrees × π ÷ 180. Common conversions: 30° = π/6 ≈ 0.5236 rad; 45° = π/4 ≈ 0.7854 rad; 90° = π/2 ≈ 1.5708 rad; 180° = π ≈ 3.1416 rad.

Radian-based formulas are mathematically simpler - the derivative of sin(x) is cos(x) only when x is in radians. Languages like JavaScript, Python and C use radians in their Math.sin(), Math.cos() functions.

A gradian (grad) divides a full circle into 400 parts (instead of 360). A right angle = 100 grad exactly, making decimal arithmetic easier. It was introduced with the metric system and is still used in some surveying instruments.

1 degree = 60 arcminutes (') = 3,600 arcseconds ("). These small units are used in navigation (1 arcminute of latitude = 1 nautical mile), astronomy (measuring angular separation of stars), and GPS precision.

1 NATO mil = 1/6400 of a full circle (360° ÷ 6400 = 0.05625°). It is used by military artillery - at 1 km range, 1 mil corresponds to approximately 1 metre of lateral displacement, simplifying range calculations.