Ever needed to compare a slow‑pulsing sensor reading with an angular speed? Converting millihertz (mHz) to radians per second (rad/s) bridges that gap, letting engineers, hobbyists, and students speak the same language.
Understanding Frequency and Its Units
Frequency measures how often something repeats in one second. The International System of Units (SI) uses the hertz (Hz) for cycles per second. When we talk about angular motion, we often switch to radians per second, which tells us how many radians an object sweeps each second.
What Is a Millihertz?
A millihertz is one‑thousandth of a hertz:
- 1 mHz = 0.001 Hz
It’s handy for very low‑frequency phenomena such as geological tremors, slow‑changing biological rhythms, or long‑period oscillations in space.
What Is a Radian Per Second?
A radian per second quantifies angular velocity. One radian is the angle created when the arc length equals the radius of a circle. Thus, 1 rad/s means the angle grows by one radian every second.
Conversion Formula
The universal link between linear frequency and angular frequency is:
ω (rad/s) = 2π × f (Hz)
Applying the milli‑prefix gives the exact factor:
1 mHz = 2π × 0.001 rad/s ≈ 0.0062831853 rad/s
Worked Example
Convert 25 mHz to rad/s
- Start with the base formula: ω = 2π × f.
- Insert the frequency in hertz: f = 25 mHz = 0.025 Hz.
- Calculate: ω = 2π × 0.025 ≈ 0.1570796 rad/s.
So, 25 mHz ≈ 0.1571 rad/s (rounded to four decimal places).
Practical Applications
- Seismology: Very low‑frequency ground motions are often reported in millihertz, while the resulting angular displacement of instruments is expressed in rad/s.
- Biomedical Engineering: Slow heart‑rate variability or circadian rhythms can be modeled in mHz, then translated to angular velocities for signal‑processing algorithms.
- Aerospace: Attitude‑control systems sometimes need to convert low‑frequency sensor data (mHz) into angular rates (rad/s) for precise maneuvering.
Millihertz to Radian Per Second Conversion Table
Each row applies the same rule: multiply millihertz by 2π × 10⁻³ to obtain radians per second.
| Millihertz (mHz) | Radian per Second (rad/s) |
|---|---|
| 1 mHz | 0.006283 rad/s |
| 2 mHz | 0.012566 rad/s |
| 5 mHz | 0.031416 rad/s |
| 10 mHz | 0.062832 rad/s |
| 20 mHz | 0.125664 rad/s |
| 50 mHz | 0.314159 rad/s |
| 100 mHz | 0.628319 rad/s |
| 500 mHz | 3.141593 rad/s |
Conclusion
Converting millihertz to radians per second is a straightforward multiplication by 2π × 10⁻³. Whether you’re analyzing slow seismic waves or fine‑tuning a spacecraft’s attitude, this conversion lets you move seamlessly between linear frequency and angular velocity. Need more conversions? Explore our suite of tools and keep your calculations flowing.