Arcminutes to Arcseconds

The degree (°) divides the full circle into 360 parts and is the everyday unit in geometry and navigation. The radian (rad) is the standard mathematical unit: 180° = π rad, so 1 rad ≈ 57.2958°. The gradian (gon) divides the circle into 400 parts, so one full turn is 400 grad = 360° and 1 grad = 0.9° — common in surveying because a right angle is exactly 100 grad.

For very small angles the degree is subdivided further: 1° = 60 arcminutes (′) and 1 arcminute = 60 arcseconds (″), so 1° = 3,600 arcseconds — used in astronomy and navigation. A turn describes one full circle (360°). For more unit pairs, use our angle conversion hub.

Angle conversions appear in maths, navigation, and engineering — degrees, radians, and gradians measure the same turn differently.

• •A full circle is 360 degrees, 2π radians (about 6.283), or 400 gradians.
• •Radians are the natural unit in calculus and physics because they simplify the formulas.
• •180 degrees equals exactly π radians — the half-turn that flips a direction.