Convert Centesimal Seconds to Semicircles
Convert Centesimal Seconds (c″) to Semicircles (sc) instantly and accurately.
Conversion Formula
sc = c″ × 5.000000000e-7
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.
About Semicircles
A semicircle equals 1/2 of a full circle - exactly π rad = 180°. GPS and GLONASS transmit satellite orbital elements with latitude and longitude in semicircles, maximising angular resolution within 32-bit signed integers: ±2³¹ units span ±π rad with ~1.46 × 10⁻⁹ rad resolution per unit. Euler's identity e^(iπ) + 1 = 0 encodes exactly 1 semicircle of rotation in the complex plane, mapping 1 to -1 - often called the most beautiful equation in mathematics. 1 semicircle = π rad = 180° = 200 grad = 3,200 NATO mils.
Quick Reference Table
| Centesimal Seconds (c″) | Semicircles (sc) |
|---|---|
| 1 c″ | 5 × 10-7 sc |
| 2 c″ | 1 × 10-6 sc |
| 5 c″ | 2.5 × 10-6 sc |
| 10 c″ | 5 × 10-6 sc |
| 25 c″ | 1.25 × 10-5 sc |
| 50 c″ | 2.5 × 10-5 sc |
| 100 c″ | 5 × 10-5 sc |