Convert Signs to Quadrants
Convert Signs (sign) to Quadrants (quad) instantly and accurately.
Conversion Formula
quad = sign × 0.3333333333
About Signs
An astrological sign equals 1/12 of a full circle - π/6 rad = exactly 30°. The zodiac divides the ecliptic into twelve 30° signs (Aries through Pisces), originating in Babylonian astronomy ~5th century BCE. Historical ecliptic longitude was expressed as sign + degrees: "Scorpio 12°" = 222°. The 30° spacing also appears in music theory: the circle of fifths has twelve equally spaced positions 30° apart, and the octave divides into 12 equal semitones. 1 sign = 30° = 1,800′ = π/6 rad = 533.3 NATO mils.
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
| Signs (sign) | Quadrants (quad) |
|---|---|
| 1 sign | 0.333333 quad |
| 2 sign | 0.666667 quad |
| 5 sign | 1.66667 quad |
| 10 sign | 3.33333 quad |
| 25 sign | 8.33333 quad |
| 50 sign | 16.6667 quad |
| 100 sign | 33.3333 quad |