Convert Milliradians per second to Revolutions per day
Convert Milliradians per second (mrad/s) to Revolutions per day (rev/d) instantly and accurately.
Conversion Formula
rev/d = mrad/s × 13.75098708
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.
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
| Milliradians per second (mrad/s) | Revolutions per day (rev/d) |
|---|---|
| 1 mrad/s | 13.751 rev/d |
| 2 mrad/s | 27.502 rev/d |
| 5 mrad/s | 68.7549 rev/d |
| 10 mrad/s | 137.51 rev/d |
| 25 mrad/s | 343.775 rev/d |
| 50 mrad/s | 687.549 rev/d |
| 100 mrad/s | 1375.1 rev/d |