Convert Gradians per second squared to Radians per second squared
Convert Gradians per second squared (gon/s²) to Radians per second squared (rad/s²) instantly and accurately.
Conversion Formula
rad/s² = gon/s² × 0.01570796327
About Gradians per second squared
The gradian per second squared (gon/s²) equals π/200 ≈ 0.015708 rad/s². The gradian (1 gon = 0.9°) is the standard angular unit in continental European surveying; robotic total stations (Leica TS16, Trimble S-Series) that report angular speed in gon/s naturally characterise servo acceleration in gon/s². DIN 18709 survey instrument calibration records angular acceleration in the gradian system. 1 gon/s² = π/200 rad/s² ≈ 0.9 °/s².
About Radians per second squared
The radian per second squared (rad/s²) is the SI coherent derived unit of angular acceleration. It appears in Newton's second law for rotation: τ = Iα, where torque τ is in N·m, moment of inertia I in kg·m², and angular acceleration α in rad/s². All engineering simulation tools (MATLAB, Simulink, ROS, FEM solvers) use rad/s² natively. A typical electric motor under full load accelerates at 10-100 rad/s². 1 rad/s² ≈ 57.296 °/s² ≈ 9.549 rpm/s.
Quick Reference Table
| Gradians per second squared (gon/s²) | Radians per second squared (rad/s²) |
|---|---|
| 1 gon/s² | 0.015708 rad/s² |
| 2 gon/s² | 0.0314159 rad/s² |
| 5 gon/s² | 0.0785398 rad/s² |
| 10 gon/s² | 0.15708 rad/s² |
| 25 gon/s² | 0.392699 rad/s² |
| 50 gon/s² | 0.785398 rad/s² |
| 100 gon/s² | 1.5708 rad/s² |