Convert Signs to Centesimal Seconds

Convert Signs (sign) to Centesimal Seconds (c″) instantly and accurately.

Conversion Formula

c″ = sign × 333333.3333

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 Centesimal Seconds

A centesimal second (c″) is 1/10,000 of a gradian - exactly π/2,000,000 rad ≈ 1.5708 × 10⁻⁶ rad. In the gradian hierarchy, 1 right angle = 100 grad = 10,000 c′ = 1,000,000 c″. High-precision total stations calibrated in gons report to 0.1-1 c″, equivalent to ~0.0324 arcseconds. Used in French, Dutch, Swiss, and Scandinavian cadastral surveys. DIN 1313 designates 10 c″ = 1 milligon (mgon). 1 c″ ≈ 0.324″ sexagesimal = π/2,000,000 rad.

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