Convert Revolutions per day to Radians per second
Convert Revolutions per day (rev/d) to Radians per second (rad/s) instantly and accurately.
Conversion Formula
rad/s = rev/d × 7.272205217e-5
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.
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.
Quick Reference Table
| Revolutions per day (rev/d) | Radians per second (rad/s) |
|---|---|
| 1 rev/d | 7.272 × 10-5 rad/s |
| 2 rev/d | 0.000145444 rad/s |
| 5 rev/d | 0.00036361 rad/s |
| 10 rev/d | 0.000727221 rad/s |
| 25 rev/d | 0.00181805 rad/s |
| 50 rev/d | 0.0036361 rad/s |
| 100 rev/d | 0.00727221 rad/s |