CPS Converter
Convert between CPS, Hz, and rad/s frequency units instantly. Free online converter for electrical engineering, physics, audio processing, and signal analysis.
About This Calculator
Our CPS Converter provides instant conversion between the three most common frequency units: hertz (Hz), cycles per second (CPS), and radians per second (rad/s). Whether you are working on AC power systems, audio equipment, motor control, signal processing, or physics problems, this tool handles frequency conversions accurately and instantly.
Frequency is a fundamental parameter in physics and engineering that measures how often a periodic event occurs per unit time. Since 1960, hertz (Hz) has been the SI standard unit for frequency, replacing the older term cycles per second (CPS). One hertz represents one complete cycle per second. Radians per second (rad/s) is the angular frequency unit used in rotational dynamics and AC circuit analysis, where one full cycle equals 2π radians. The conversion between these units follows straightforward formulas: 1 Hz = 1 CPS, and 1 Hz = 2π rad/s ≈ 6.283 rad/s. Simply enter a value, select the source unit and target unit, and the converter displays the result instantly. The tool supports bidirectional conversion between all three units.
Key Conversion Factors
- 1 Hz = 1 CPS: The two units are numerically equivalent; Hz is the modern SI name
- 1 Hz = 2π rad/s ≈ 6.283 rad/s: One complete cycle equals 2π radians
- 1 rad/s ≈ 0.1592 Hz: One radian per second equals about 0.1592 cycles per second
Common Frequency Ranges by Application
- AC Power: 50 Hz (Europe, Asia, Africa, Australia) and 60 Hz (Americas, parts of Asia) — corresponding to 314.16 rad/s and 376.99 rad/s respectively
- Audio: 20 Hz to 20,000 Hz (human hearing range), with musical note A4 tuned to 440 Hz
- Radio Communications: 88–108 MHz (FM broadcast), 2.4–5 GHz (WiFi and Bluetooth)
- Industrial: Motor speeds in RPM (revolutions per minute) convert through rad/s for control system design
Regional Notes
Frequency conversion is a globally standardized concept in physics and engineering. The SI unit hertz (Hz) is used worldwide, including in India, the United States, and the United Kingdom. However, practical applications differ by region: India and the UK use 50 Hz for mains power, while the United States uses 60 Hz. Engineers and technicians in all regions need to convert between Hz and rad/s for motor control, AC circuit analysis, and vibration testing regardless of the local power frequency.
Frequently Asked Questions
What is the difference between Hz, CPS, and rad/s?
Hertz (Hz) and cycles per second (CPS) are equivalent units representing the number of complete cycles per second. Radians per second (rad/s) measures angular frequency where one complete cycle equals 2pi radians. So 1 Hz = 1 CPS = 2pi rad/s ≈ 6.283 rad/s. Hz is the SI unit, while CPS is an older term.
How do I convert Hz to rad/s?
To convert Hz to rad/s, multiply by 2pi (approximately 6.283): rad/s = Hz x 2pi. For example, 60 Hz = 60 x 2pi = 376.99 rad/s. This conversion is essential in AC electrical engineering, motor design, and control systems where angular frequency is needed.
What are common frequency values?
Common frequencies: 50 Hz (Europe/Asia power grid), 60 Hz (Americas power grid), 440 Hz (musical note A4 tuning), 20-20,000 Hz (human hearing range), 88-108 MHz (FM radio), 2.4-5 GHz (WiFi). Rad/s is commonly used in physics: 314.16 rad/s corresponds to 50 Hz, 376.99 rad/s to 60 Hz.
Why use rad/s instead of Hz?
Rad/s is preferred in physics and engineering for angular velocity and AC circuit analysis because it simplifies mathematical relationships. In formulas like omega = 2pif, using rad/s avoids repeatedly writing 2pi. It is the natural unit for derivatives of sinusoidal functions and phasor analysis.
Is CPS the same as Hz?
Yes, CPS (cycles per second) and Hz (hertz) are exactly the same unit. The term hertz replaced CPS in 1960 when the SI system was established, named after physicist Heinrich Hertz. Some older equipment and textbooks may still use CPS, but Hz is the modern standard.
What is the formula for frequency conversion?
The conversion formulas are: 1 Hz = 1 CPS, 1 rad/s = 1/(2pi) Hz ≈ 0.1592 Hz, and 1 Hz = 2pi rad/s ≈ 6.283 rad/s. To convert any frequency to another unit, first convert to Hz, then multiply or divide by the appropriate conversion factor.
How is frequency used in real-world applications?
Frequency measurement is critical in: AC power (50/60 Hz), audio engineering (sample rates 44.1-192 kHz), radio communications (MHz-GHz), CPU clock speeds (GHz), vibration analysis (Hz-kHz), medical imaging (MHz ultrasound), and control systems (rad/s for motor speed control).