Convert Radians per second to Gradians per second
Convert Radians per second (rad/s) to Gradians per second (gon/s) instantly and accurately.
Conversion Formula
gon/s = rad/s × 63.66197724
About Radians per second
The radian per second (rad/s) is the SI coherent derived unit of angular velocity. It appears naturally in all analytical mechanics: angular frequency ω = 2πf; torque-power relation P = τω; pendulum natural frequency ωₙ = √(g/L); Bode plot frequency axis. All SI engineering software (FEM solvers, robotics middleware ROS, control system toolboxes) uses rad/s natively. Earth's rotation rate Ω⊕ = 7.292 × 10⁻⁵ rad/s. Power electronics PWM carriers at 2-20 kHz correspond to 12566-125664 rad/s. 1 rad/s ≈ 9.5493 rpm = 57.296 °/s.
About Gradians per second
The gradian per second (gon/s) equals π/200 rad/s ≈ 0.01571 rad/s, where the gradian (1 gon = 0.9°) divides the right angle into 100 equal parts. Introduced during the French Revolution as part of decimal reform, the gradian remains the standard angular unit in European continental surveying: total stations (Leica TS16, Trimble S9) sold in Germany, France, and Scandinavia default to gon; Austrian and Swiss cadastral land registers record all bearings in gon. DIN 18709 specifies survey work in gon; ISO 80000-3 acknowledges the unit. 1 gon/s = π/200 rad/s ≈ 0.9 °/s ≈ 0.15 rpm.
Quick Reference Table
| Radians per second (rad/s) | Gradians per second (gon/s) |
|---|---|
| 1 rad/s | 63.662 gon/s |
| 2 rad/s | 127.324 gon/s |
| 5 rad/s | 318.31 gon/s |
| 10 rad/s | 636.62 gon/s |
| 25 rad/s | 1591.55 gon/s |
| 50 rad/s | 3183.1 gon/s |
| 100 rad/s | 6366.2 gon/s |