Ever needed to compare a rotating shaft’s speed with a radio‑frequency signal? Converting degrees per second (deg/s) to kilohertz (kHz) bridges the gap between angular motion and ordinary frequency. Below you’ll find the exact factor, a simple formula, and a ready‑to‑use table so you can switch units in a single glance.
What Is a Degree Per Second?
A degree per second measures how fast an angle changes. One deg/s means the angle grows by one degree every second. In a full circle there are 360 degrees, so 360 deg/s equals one complete revolution per second.
What Is a Kilohertz?
A kilohertz is a thousand cycles per second. One kHz equals 1,000 Hz, and one hertz (Hz) is one cycle per second. It’s the standard unit for radio, audio, and digital clock rates.
Linking the Two Units
Because a full cycle corresponds to 360 degrees, we can treat angular speed as a frequency:
- 1 cycle = 360 degrees
- 1 Hz = 1 cycle / second = 360 deg/s ÷ 360 = 1 deg/s ÷ 360
Therefore:
1 deg/s = 1 / 360 Hz = 1 / 360 000 kHz
Exact Conversion Factor
The precise factor is:
1 deg/s = 0.0000027778 kHz
In formula form:
kHz = (deg/s) ÷ 360 000
Worked Example
Suppose a motor spins at 45 deg/s. To express this speed in kilohertz:
- Divide by 360 000:
45 ÷ 360 000 = 0.000125 kHz - Result: 45 deg/s ≈ 0.000125 kHz
This tiny kHz value shows that angular speeds are usually far slower than typical radio frequencies.
Practical Applications
- Motor control: Engineers compare shaft speeds with control‑loop frequencies.
- Signal processing: Converting sensor rotation rates to a frequency domain for FFT analysis.
- Robotics: Matching joint angular velocities to communication bus rates.
Degree Per Second to Kilohertz Conversion Table
Each row applies the same rule: multiply degrees per second by 0.0000027778 kHz/deg/s. Values are rounded to the nearest ten‑thousandth of a kilohertz.
| Degree per Second (deg/s) | Kilohertz (kHz) |
|---|---|
| 1 deg/s | 0.0000027778 kHz |
| 2 deg/s | 0.0000055556 kHz |
| 5 deg/s | 0.0000138889 kHz |
| 10 deg/s | 0.0000277778 kHz |
| 20 deg/s | 0.0000555556 kHz |
| 50 deg/s | 0.0001388889 kHz |
| 100 deg/s | 0.0002777778 kHz |
| 500 deg/s | 0.0013888889 kHz |
Key Takeaway
Converting deg/s to kHz is a simple division by 360 000. Keep the factor 0.0000027778 kHz per deg/s handy, and you’ll instantly translate rotational speeds into the language of frequency.
Ready to apply this conversion in your next project? Plug the factor into your spreadsheets, calculators, or code and let the numbers do the work.