CPS Calculator
Convert cycles per second (CPS) to hertz, RPM, radians per second, and other frequency units
Frequency Converter
Conversion Result
0 Hz
0 cps = 0 Hz
From: Cycles per Second (cps)
To: Hertz (Hz)
Type: Frequency conversion
Common Frequency Conversions
1 cps = 1 Hz
Cycles per second equals hertz
Cycles per second equals hertz
1 cps = 2π rad/s
≈ 6.283 radians per second
≈ 6.283 radians per second
1 cps = 360°/s
Degrees per second
Degrees per second
1 cps = 60 cpm
Cycles per minute
Cycles per minute
60 Hz = 3600 RPM
Common AC frequency
Common AC frequency
1 kHz = 1000 cps
Audio frequency range
Audio frequency range
Frequency Applications
Audio & Sound
- • 20 Hz - 20 kHz: Human hearing
- • 440 Hz: Musical note A4
- • 8-48 kHz: Digital audio
Electrical
- • 50/60 Hz: AC power grid
- • 2.4 GHz: WiFi & Bluetooth
- • 1-6 GHz: Mobile networks
Mechanical
- • 600-3600 RPM: Motors
- • 0.5-100 Hz: Vibrations
- • 1-10 Hz: Seismic waves
Frequency Unit Types
Linear Frequency:
- • Hertz (Hz)
- • Kilohertz (kHz)
- • Megahertz (MHz)
- • Gigahertz (GHz)
Angular Frequency:
- • Radians per second (rad/s)
- • Degrees per second (°/s)
- • Revolutions per minute (RPM)
Time-based:
- • Cycles per second (cps)
- • Cycles per minute (cpm)
Understanding Frequency Units
What is Frequency?
Frequency is a measure of how often a repeating event occurs per unit of time. It's fundamental in physics, engineering, and many other fields, describing everything from sound waves to electrical signals to mechanical vibrations.
CPS vs Hertz
- •CPS (Cycles per Second): Historical unit for frequency
- •Hertz (Hz): Modern SI unit, identical to CPS
- •Relationship: 1 cps = 1 Hz exactly
Key Conversion Formulas
Angular Frequency
• ω (rad/s) = 2π × f (Hz)
• 1 cps = 2π rad/s ≈ 6.283 rad/s
• 1 cps = 2π rad/s ≈ 6.283 rad/s
Rotational Speed
• RPM = Hz × 60
• 1 Hz = 60 RPM
• 1 Hz = 60 RPM
Degrees per Second
• °/s = Hz × 360
• 1 Hz = 360°/s
• 1 Hz = 360°/s
Frequency Reference Table
| CPS/Hz | RPM | rad/s | °/s | Application |
|---|---|---|---|---|
| 0.5 | 30 | 3.14 | 180 | Slow rotation |
| 1 | 60 | 6.28 | 360 | 1 revolution/second |
| 50 | 3,000 | 314 | 18,000 | EU power grid |
| 60 | 3,600 | 377 | 21,600 | US power grid |
| 440 | 26,400 | 2,765 | 158,400 | Musical note A4 |
| 1,000 | 60,000 | 6,283 | 360,000 | 1 kilohertz |
| 1,000,000 | 60×10⁶ | 6.28×10⁶ | 3.6×10⁸ | 1 megahertz |