Convert Signs to Radians
Convert Signs (sign) to Radians (rad) instantly and accurately.
Conversion Formula
rad = sign × 0.5235987756
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 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
| Signs (sign) | Radians (rad) |
|---|---|
| 1 sign | 0.523599 rad |
| 2 sign | 1.0472 rad |
| 5 sign | 2.61799 rad |
| 10 sign | 5.23599 rad |
| 25 sign | 13.09 rad |
| 50 sign | 26.1799 rad |
| 100 sign | 52.3599 rad |