Convert Radians per second to Revolutions per day
Convert Radians per second (rad/s) to Revolutions per day (rev/d) instantly and accurately.
Conversion Formula
rev/d = rad/s × 13750.98708
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 Revolutions per day
The revolution per day (rev/d) equals π/43200 rad/s ≈ 7.272 × 10⁻⁵ rad/s, the scale of planetary rotation and orbital mechanics. Earth spins at 1.00274 rev/day (sidereal); Mars at 1.027 rev/day (sol = 24 h 37 min); Jupiter at 2.417 rev/day. Geostationary satellites orbit at exactly 1 rev/solar day; Molniya HEO satellites at 2 rev/day. The Moon is tidally locked at 1/27.322 rev/day. IERS Bulletin A tracks Earth's deviation from 1 rev/solar day to 0.1 ms precision. 1 rev/d ≈ 7.272 × 10⁻⁵ rad/s ≈ 6.944 × 10⁻³ rpm.
Quick Reference Table
| Radians per second (rad/s) | Revolutions per day (rev/d) |
|---|---|
| 1 rad/s | 13751 rev/d |
| 2 rad/s | 27502 rev/d |
| 5 rad/s | 68754.9 rev/d |
| 10 rad/s | 137510 rev/d |
| 25 rad/s | 343775 rev/d |
| 50 rad/s | 687549 rev/d |
| 100 rad/s | 1375100 rev/d |