Convert Degrees to Radians

Convert Degrees (°) to Radians (rad) instantly and accurately.

Conversion Formula

rad = ° × 0.01745329252

About Degrees

The degree (°) is the most widely used angle unit in everyday life, tracing to Babylonian astronomy ~300 BCE - the ecliptic was divided into 360 parts because the sexagesimal base-60 system made 360 highly divisible (by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20). Each degree divides into 60 arcminutes and 3,600 arcseconds. The degree dominates practical work: compass bearings, geographic coordinates (latitude ±90°, longitude ±180°), wind direction, polygon angles, and engineering drawings. Calculus uses radians because sin(x) ≈ x only holds in radians. 1° = π/180 rad ≈ 17.453 mrad.

About Radians

The radian (rad) is the SI unit of plane angle, defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. A full circle = 2π rad; a right angle = π/2 rad. The radian is dimensionless (arc length / radius), so it can be omitted in equations. All calculus and physics formulas are simplest in radians: d/dx(sin x) = cos x holds only in radians; Taylor series sin x = x − x³/6 + x⁵/120 hold only for x in radians; angular frequency ω = 2πf gives energy E = ħω. 1 rad = 180°/π ≈ 57.2958° ≈ 206,264.8″.

Quick Reference Table

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