Convert Quadrants to Degrees

Convert Quadrants (quad) to Degrees (°) instantly and accurately.

Conversion Formula

° = quad × 90

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.

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.

Quick Reference Table

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