An angle converter moves a value between the ways we measure rotation: degrees (a circle in 360 parts), radians (the natural maths unit, 2π to a circle), gradians (400 to a circle), and the fine subdivisions arcminutes and arcseconds. It converts your value into a base unit — degrees — and back out. The conversion people reach for most is degrees ↔ radians, since calculators and code work in radians while everyday angles are quoted in degrees.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the exact circle definitions, recomputed in code.
How the conversion works
Each unit equals a fixed number of degrees: a radian is 57.29578°, a gradian 0.9°, an arcminute one-sixtieth of a degree. Multiply your value by the "from" unit's degrees-per-unit to reach degrees, then divide by the "to" unit's. The two facts to anchor on: a half circle is 180° = π radians, and a full circle is 360° = 2π radians = 400 gradians.
Worked example — 180° in other units
Scenario: convert 180 degrees (a half circle) to other angle units.
180° is exactly π radians (about 3.14159), 200 gradians, or half a turn. The everyday cases follow the same rule: 90° is π/2 ≈ 1.5708 radians (100 gradians), one radian is 57.29578°, and a full turn is 2π ≈ 6.28319 radians. The converter shows every unit at once — handy when you need radians for code but think in degrees.
Frequently Asked Questions
× π/180. 180° = π ≈ 3.14159; 90° = 1.5708.
180 ÷ π ≈ 57.29578°. A full circle is 2π ≈ 6.2832 rad.
400 to a circle: 1 grad = 0.9°. 90° = 100 grad.
1° = 60′ = 3600″. Used in astronomy & surveying.
2π ≈ 6.28319 (= 360° = 400 grad).