Angle Converter (degrees, radians, gradians, turns)

Six angle units explained

Degrees (°): full circle = 360°. Most common everyday unit. Right angle = 90°, half-turn = 180°. Used in geometry, navigation, physics introductions, daily speech.

Radians (rad): full circle = 2π ≈ 6.283 rad. SI/scientific unit; defined as the arc length divided by radius for a unit circle. All math and physics formulas use radians (sin, cos, tan natively expect radians in most programming languages).

Gradians (gon, grad): full circle = 400 grad. Right angle = 100 grad — the appeal: decimal-friendly, used in surveying and some European engineering contexts.

Turns: full circle = 1 turn. Half-turn = 0.5. Used in physics for cyclic motion and in CSS (transform: rotate(0.25turn) = 90°).

Arcminutes ('): 1° = 60 arcmin. Used in navigation (1 nautical mile ≈ 1 arcmin of latitude) and astronomy.

Arcseconds (''): 1° = 3600 arcsec, 1 arcmin = 60 arcsec. Astronomy uses arcseconds extensively (parallax, telescope resolution).

Common conversions to memorize

180° = π rad ≈ 3.14159 rad. The single most useful conversion in math and physics. Most other conversions follow from this.

90° = π/2 rad ≈ 1.5708 rad (right angle).

60° = π/3 ≈ 1.047 rad. 45° = π/4 ≈ 0.785 rad. 30° = π/6 ≈ 0.524 rad. These three are the 'special angles' from trigonometry.

1° = 60 arcmin = 3600 arcsec. 1 arcmin = 60 arcsec.

1 turn = 360° = 2π rad = 400 grad.

Where each unit is preferred

Programming and physics: radians. JavaScript's Math.sin, Math.cos, Math.tan all expect radians. Convert from degrees via × Math.PI / 180.

Education and everyday: degrees. Most students learn trigonometry in degrees. Construction, navigation, and casual measurement all use degrees.

Engineering surveys (Europe): gradians. A 100-gradian right angle simplifies decimal arithmetic in field calculations.

Astronomy: arcminutes and arcseconds for sky positions. Parallax distances are quoted in arcseconds.

CSS animations: degrees, radians, or turns. transform: rotate(45deg) and rotate(0.125turn) are equivalent — pick whichever reads more naturally.