Convert Centesimal Seconds to Radians
Convert Centesimal Seconds (c″) to Radians (rad) instantly and accurately.
Conversion Formula
rad = c″ × 1.570796327e-6
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 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″.
Quick Reference Table
| Centesimal Seconds (c″) | Radians (rad) |
|---|---|
| 1 c″ | 1.571 × 10-6 rad |
| 2 c″ | 3.142 × 10-6 rad |
| 5 c″ | 7.854 × 10-6 rad |
| 10 c″ | 1.571 × 10-5 rad |
| 25 c″ | 3.927 × 10-5 rad |
| 50 c″ | 7.854 × 10-5 rad |
| 100 c″ | 0.00015708 rad |