Convert Radians to Quadrants

Convert Radians (rad) to Quadrants (quad) instantly and accurately.

Conversion Formula

quad = rad × 0.6366197724

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″.

About Quadrants

A quadrant equals 1/4 of a full circle - π/2 rad = 90°, the right angle. Perpendicularity underpins Euclidean geometry, the Pythagorean theorem, and Cartesian coordinate systems. In AC electrical engineering, voltage and current in purely reactive circuits are exactly 90° out of phase, defining reactive power in VAr. The four quadrants of the unit circle determine the sign of sine, cosine, and tangent. GPS orbital elements encode latitude in semicircles bounded by ±1 quadrant = ±90°. 1 quadrant = 90° = 100 grad = π/2 rad = 1,600 NATO mils.

Quick Reference Table

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