Convert Revolutions per day to Milliradians per second
Convert Revolutions per day (rev/d) to Milliradians per second (mrad/s) instantly and accurately.
Conversion Formula
mrad/s = rev/d × 0.07272205217
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 Milliradians per second
The milliradian per second (mrad/s) is 10⁻³ rad/s, used in precision guidance and antenna pointing. Phased-array radar beam steering rates for track-while-scan modes are typically 10-1000 mrad/s. LEO Earth-observation satellites (Sentinel-2, WorldView-3) manoeuvre between imaging targets at 5-20 mrad/s and slew at 50-200 mrad/s. Industrial robot wrist joints (KUKA, Fanuc) operate at 17-175 mrad/s. Optical encoders (Heidenhain RON 905) can measure angular velocity to 0.1 mrad/s accuracy. 1 mrad/s = 10⁻³ rad/s ≈ 0.0573 °/s ≈ 9.549 × 10⁻³ rpm.
Quick Reference Table
| Revolutions per day (rev/d) | Milliradians per second (mrad/s) |
|---|---|
| 1 rev/d | 0.0727221 mrad/s |
| 2 rev/d | 0.145444 mrad/s |
| 5 rev/d | 0.36361 mrad/s |
| 10 rev/d | 0.727221 mrad/s |
| 25 rev/d | 1.81805 mrad/s |
| 50 rev/d | 3.6361 mrad/s |
| 100 rev/d | 7.27221 mrad/s |