Convert Signs to Centesimal Minutes

Convert Signs (sign) to Centesimal Minutes (c′) instantly and accurately.

Conversion Formula

c′ = sign × 3333.333333

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 Minutes

A centesimal minute (c′) is 1/100 of a gradian - exactly π/20,000 rad ≈ 1.5708 × 10⁻⁴ rad (= 0.9 sexagesimal arcminutes). Also designated cgon (centigon) in ISO/DIN standards. Total stations in the grad system display readings to 1 c′ or 0.1 c′; a right angle = 100 grad = 10,000 c′. A 1% slope ≈ 0.6366 grad ≈ 63.66 c′ - a simple calculation that makes the centesimal minute popular in road and railway alignment. 1 c′ = 0.9′ = 54″ = π/20,000 rad.

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