Convert Radians to Signs
Convert Radians (rad) to Signs (sign) instantly and accurately.
Conversion Formula
sign = rad × 1.909859317
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 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.
Quick Reference Table
| Radians (rad) | Signs (sign) |
|---|---|
| 1 rad | 1.90986 sign |
| 2 rad | 3.81972 sign |
| 5 rad | 9.5493 sign |
| 10 rad | 19.0986 sign |
| 25 rad | 47.7465 sign |
| 50 rad | 95.493 sign |
| 100 rad | 190.986 sign |