Ever needed to compare a rotating sensor’s speed with a radio‑frequency signal? Converting degrees per second (deg/s) to millihertz (mHz) bridges the gap between angular motion and ordinary frequency, letting you speak the same language across engineering domains.
Frequency Basics: From Angles to Cycles
Frequency measures how often something repeats in one second. In the International System, the base unit is the hertz (Hz), equal to one complete cycle per second. Two common ways to express that repeat rate are:
- Degree per second (deg/s) – the angular distance covered each second. One full circle equals 360°, so 360 deg/s equals one cycle per second (1 Hz).
- Millihertz (mHz) – one‑thousandth of a hertz. It’s handy when dealing with very low‑frequency phenomena.
Exact Conversion Factor
The relationship is straightforward: 1 deg/s = 2.7778 mHz. This factor comes from the fact that 1 Hz = 360 deg/s and 1 Hz = 1 000 mHz.
How the Formula Is Built
Start with the definition of a hertz in terms of degrees:
- 1 Hz = 360 deg/s → 1 deg/s = 1 Hz ÷ 360.
- Convert hertz to millihertz: 1 Hz = 1 000 mHz.
- Combine the steps:
1 deg/s = (1 000 mHz) ÷ 360 = 2.777777… mHz
Rounded to four decimal places, the factor is 2.7778 mHz per deg/s.
Worked Example: From a Gyroscope to Millihertz
Imagine a gyroscope spins at 45 deg/s. To express that speed in millihertz:
- Multiply by the conversion factor: 45 deg/s × 2.7778 mHz/deg/s.
- Result: 125.001 mHz (rounded to three decimal places).
So the gyroscope’s rotation is equivalent to a 0.125 Hz signal, or 125 mHz.
Practical Situations Where This Conversion Shines
- Robotics: Align motor angular velocity with sensor sampling rates expressed in hertz.
- Astronomy: Compare the slow precession of a telescope mount (deg/s) with the low‑frequency drift of a radio telescope (mHz).
- Audio Engineering: Relate the sweep speed of a rotary potentiometer to sub‑audible modulation frequencies.
Degree Per Second to Millihertz Conversion Table
Each row applies the same rule: multiply degrees per second by 2.7778 to obtain millihertz (rounded to four decimal places).
| Degree Per Second (deg/s) | Millihertz (mHz) |
|---|---|
| 1 deg/s | 2.7778 mHz |
| 2 deg/s | 5.5556 mHz |
| 5 deg/s | 13.8889 mHz |
| 10 deg/s | 27.7778 mHz |
| 20 deg/s | 55.5556 mHz |
| 50 deg/s | 138.8889 mHz |
| 100 deg/s | 277.7778 mHz |
| 500 deg/s | 1,388.8889 mHz |
Quick Reference Cheat Sheet
- 1 deg/s = 2.7778 mHz
- 1 mHz = 0.36 deg/s
- Use the factor 2.7778 for fast mental conversions.
Conclusion
Converting between degrees per second and millihertz is a matter of remembering that a full circle (360°) equals one hertz, and that one hertz contains 1 000 millihertz. With the factor 2.7778 mHz per deg/s, you can translate angular speeds into ordinary frequency instantly. Need more conversion tools or a custom calculator? Explore our suite of unit converters today and keep your projects moving at the right pace.