Convert Signs to Gradians
Convert Signs (sign) to Gradians (grad) instantly and accurately.
Conversion Formula
grad = sign × 33.33333333
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 Gradians
A gradian (grad), also called a gon (ISO 31/DIN), equals 1/400 of a full circle - π/200 rad = 0.9°. Its main advantage: a right angle = exactly 100 grad, simplifying complementary and supplementary angle arithmetic. Introduced during the French Revolution as part of decimal angle reform. Surveying in France, the Netherlands, Switzerland, and Scandinavia uses gradians; professional total stations display both degrees and gons. A 1% slope ≈ 0.6366 grad. 1 grad = 0.9° = 54′ = π/200 rad; 400 grad = 360° = one full circle.
Quick Reference Table
| Signs (sign) | Gradians (grad) |
|---|---|
| 1 sign | 33.3333 grad |
| 2 sign | 66.6667 grad |
| 5 sign | 166.667 grad |
| 10 sign | 333.333 grad |
| 25 sign | 833.333 grad |
| 50 sign | 1666.67 grad |
| 100 sign | 3333.33 grad |