UnitsConverter

Cycles per Second to Radians per Second Converter

Convert cps to rad/s with our free online frequency converter.

Quick Answer

1 Cycles per Second = 6.283185 rad/s

Formula: Cycles per Second ร— conversion factor = Radians per Second

Use the calculator below for instant, accurate conversions.

Our Accuracy Guarantee

All conversion formulas on UnitsConverter.io have been verified against NIST (National Institute of Standards and Technology) guidelines and international SI standards. Our calculations are accurate to 10 decimal places for standard conversions and use arbitrary precision arithmetic for astronomical units.

Last verified: December 2025Reviewed by: Sam Mathew, Software Engineer

Cycles per Second to Radians per Second Calculator

How to Use the Cycles per Second to Radians per Second Calculator:

  1. Enter the value you want to convert in the 'From' field (Cycles per Second).
  2. The converted value in Radians per Second will appear automatically in the 'To' field.
  3. Use the dropdown menus to select different units within the Frequency category.
  4. Click the swap button (โ‡Œ) to reverse the conversion direction.
Share:

How to Convert Cycles per Second to Radians per Second: Step-by-Step Guide

Converting Cycles per Second to Radians per Second involves multiplying the value by a specific conversion factor, as shown in the formula below.

Formula:

rad/s = cps ร— 6.28319

Example Calculation:

1 cps = 6.283185 rad/s

Disclaimer: For Reference Only

These conversion results are provided for informational purposes only. While we strive for accuracy, we make no guarantees regarding the precision of these results, especially for conversions involving extremely large or small numbers which may be subject to the inherent limitations of standard computer floating-point arithmetic.

Not for professional use. Results should be verified before use in any critical application. View our Terms of Service for more information.

Need to convert to other frequency units?

View all Frequency conversions โ†’
๐Ÿ“Š Frequency Table

Print-friendly conversion reference

๐Ÿ“‹ Unit Symbols

Copy cps & rad/s symbols

What is a Cycles per Second and a Radians per Second?

1 cps = 1 Hz = 1 cycle per second = 1 complete oscillation per second

1 rad/s = 1 radian per second = 1/(2ฯ€) Hz โ‰ˆ 0.159155 Hz

Relationship to Hz:

  • ฯ‰ (rad/s) = 2ฯ€f (Hz)
  • f (Hz) = ฯ‰/(2ฯ€) (rad/s)

Key relationship: 2ฯ€ rad/s = 1 Hz (one complete cycle)

Note: The Cycles per Second is part of the imperial/US customary system, primarily used in the US, UK, and Canada for everyday measurements. The Radians per Second belongs to the imperial/US customary system.

History of the Cycles per Second and Radians per Second

Before 1960: "Cycles per second" was the standard term

  • Common abbreviations: c/s, c.p.s., cps, ~/s

1960: Renamed to "hertz" (Hz)

  • Honors Heinrich Hertz (1857-1894)
  • Adopted at 11th CGPM (General Conference on Weights and Measures)
  • Simplified terminology and standardized notation

Why the change?

  • Shorter, more convenient
  • Honors a pioneering physicist
  • Consistent with other SI units named after scientists (ampere, watt, volt, etc.)
  • International standardization

Common Uses and Applications: cps vs rad/s

Explore the typical applications for both Cycles per Second (imperial/US) and Radians per Second (imperial/US) to understand their common contexts.

Common Uses for cps

(Historical & Current)

Historical Technical Documents: Pre-1960 radio, electronics, and acoustics literature. Some Fields Still Use "cycles": Audio engineering may say "cycles" colloquially. Education: Teaching frequency concepts before introducing Hz notation. Older Equipment: Vintage test equipment labeled in cps.

When to Use rad/s

Physics: Simple harmonic motion, pendulums, springs, wave equations. Electrical Engineering: AC circuit analysis, phasors, impedance. Mechanical Engineering: Rotational dynamics, angular velocity, vibration analysis. Control Systems: Transfer functions, frequency response, stability analysis.

Additional Unit Information

About Cycles per Second (cps)

Is cps the same as Hz?

Yes, exactly the same:

  • 1 cps = 1 Hz
  • 1 kilocycles per second (kcps or kc/s) = 1 kHz
  • 1 megacycles per second (Mcps or Mc/s) = 1 MHz

Only difference: Terminology and era

  • cps: Used before 1960
  • Hz: Used from 1960 onwards (current standard)

Example conversions:

  • 60 cps = 60 Hz (AC power)
  • 1000 cps = 1 kHz (audio frequency)
  • 100,000 cps = 100 kHz (AM radio range)

cps to Hz converter โ†’

Why was cps changed to hertz?

Reasons for the 1960 change:

  1. Brevity: "Hz" is shorter than "cycles per second"
  2. Honor: Named after Heinrich Hertz who proved electromagnetic wave existence
  3. Standardization: Consistent with ampere, watt, volt, newton, pascal
  4. International: Single symbol understood globally
  5. Simplicity: Easier for metric prefixes (kHz, MHz, GHz vs kcps, Mcps, Gcps)

The change was purely nomenclature - the measurement itself remained identical.

When do I still see "cycles per second"?

Where you might encounter cps:

Historical documents:

  • Pre-1960 radio manuals
  • Vintage audio equipment
  • Old electrical engineering textbooks

Colloquial use:

  • Audio engineers may say "cycles" informally
  • Explaining frequency concepts to beginners
  • When emphasizing the cyclic nature

Vintage equipment:

  • Old oscilloscopes
  • Antique signal generators
  • Historical test equipment

Recommendation: Use Hz in all modern contexts. Only use cps when discussing historical equipment or documents.

How do I convert kc/s (kilocycles per second) to Hz?

Formula: Hz = kc/s ร— 1,000

Examples:

  • 1 kc/s = 1,000 Hz = 1 kHz
  • 10 kc/s = 10,000 Hz = 10 kHz
  • 1000 kc/s = 1,000,000 Hz = 1 MHz

Old radio terminology:

  • AM radio: 550-1600 kc/s = 550-1600 kHz
  • Shortwave: 3-30 Mc/s = 3-30 MHz

kHz to Hz converter โ†’

What is Mc/s (megacycles per second)?

Mc/s = Megacycles per second (historical term)

Modern equivalent: MHz (megahertz)

Conversion: 1 Mc/s = 1 MHz = 1,000,000 Hz

Historical usage:

  • FM radio: 88-108 Mc/s โ†’ now 88-108 MHz
  • VHF TV: 54-216 Mc/s โ†’ now 54-216 MHz
  • Old radio communications

Old abbreviations:

  • Mc/s, Mc, Mcps all meant megacycles per second
  • Now standardized as MHz

MHz to Hz converter โ†’

About Radians per Second (rad/s)

How do I convert rad/s to Hz?

Formula: Hz = rad/s รท (2ฯ€)

Examples:

  • 2ฯ€ rad/s = 1 Hz
  • 6.28 rad/s โ‰ˆ 1 Hz
  • 377 rad/s = 60 Hz (US power frequency)
  • 314 rad/s = 50 Hz (European power frequency)

Reverse: rad/s = Hz ร— 2ฯ€

rad/s to Hz converter โ†’

What is 2ฯ€ rad/s?

2ฯ€ rad/s = 1 Hz = 1 cycle per second

This is the key relationship:

  • One complete cycle = 2ฯ€ radians = 360 degrees
  • So 2ฯ€ rad/s = one full rotation per second
  • = 1 Hz
  • = 60 RPM

Example:

  • Object rotating at 2ฯ€ rad/s completes exactly 1 full rotation every second

How do I convert rad/s to RPM?

Formula: RPM = rad/s ร— (60/2ฯ€) โ‰ˆ rad/s ร— 9.549

Examples:

  • 1 rad/s = 9.55 RPM
  • 10 rad/s = 95.5 RPM
  • 100 rad/s = 955 RPM

Reverse: rad/s = RPM ร— (2ฯ€/60) โ‰ˆ RPM ร— 0.1047

Derivation:

  • 1 revolution = 2ฯ€ radians
  • 1 minute = 60 seconds
  • So: rad/s โ†’ rev/s โ†’ rev/min
  • rad/s ร— (1 rev / 2ฯ€ rad) ร— (60 s / 1 min) = rad/s ร— 60/(2ฯ€) RPM

rad/s to RPM converter โ†’

What is 377 rad/s?

377 rad/s = 60 Hz (US electrical power frequency)

Calculation: ฯ‰ = 2ฯ€f = 2ฯ€ ร— 60 โ‰ˆ 376.99 rad/s

This is the angular frequency of:

  • AC power in North America
  • 60 Hz electrical systems
  • Standard wall outlet frequency (in angular terms)

Used in electrical engineering for AC circuit calculations, phasor analysis, and impedance.

When should I use rad/s instead of Hz?

Use rad/s when:

  • Doing physics/engineering calculations
  • Working with differential equations
  • Analyzing AC circuits
  • Using transfer functions
  • Calculating angular displacement
  • Working with phasors

Use Hz when:

  • Describing oscillation rate to general audience
  • Specifying radio frequencies
  • Measuring audio frequencies
  • General frequency specifications
  • Non-technical contexts

Why rad/s in calculations?

  • Simplifies formulas: x = A sin(ฯ‰t) instead of x = A sin(2ฯ€ft)
  • Direct angular displacement: ฮธ = ฯ‰t
  • Natural for calculus: dx/dt, dยฒx/dtยฒ

What's the difference between rad/s and degrees/s?

Conversion: 1 rad/s = 180/ฯ€ deg/s โ‰ˆ 57.296 deg/s

Radians (rad/s):

  • Mathematical standard
  • Used in calculus and physics
  • 2ฯ€ rad = one full rotation
  • Natural for trigonometric functions

Degrees (deg/s):

  • Intuitive for visualization
  • 360ยฐ = one full rotation
  • Common in navigation, astronomy
  • Easier for non-technical communication

Example:

  • 1 rad/s = 57.3 degrees per second
  • ฯ€ rad/s = 180 degrees per second
  • 2ฯ€ rad/s = 360 degrees per second = 1 revolution per second

For engineering and physics calculations, use rad/s.

Conversion Table: Cycles per Second to Radians per Second

Cycles per Second (cps)Radians per Second (rad/s)
0.53.142
16.283
1.59.425
212.566
531.416
1062.832
25157.08
50314.159
100628.319
2501,570.796
5003,141.593
1,0006,283.185

People Also Ask

How do I convert Cycles per Second to Radians per Second?

To convert Cycles per Second to Radians per Second, enter the value in Cycles per Second in the calculator above. The conversion will happen automatically. Use our free online converter for instant and accurate results. You can also visit our frequency converter page to convert between other units in this category.

Learn more โ†’

What is the conversion factor from Cycles per Second to Radians per Second?

The conversion factor depends on the specific relationship between Cycles per Second and Radians per Second. You can find the exact conversion formula and factor on this page. Our calculator handles all calculations automatically. See the conversion table above for common values.

Can I convert Radians per Second back to Cycles per Second?

Yes! You can easily convert Radians per Second back to Cycles per Second by using the swap button (โ‡Œ) in the calculator above, or by visiting our Radians per Second to Cycles per Second converter page. You can also explore other frequency conversions on our category page.

Learn more โ†’

What are common uses for Cycles per Second and Radians per Second?

Cycles per Second and Radians per Second are both standard units used in frequency measurements. They are commonly used in various applications including engineering, construction, cooking, and scientific research. Browse our frequency converter for more conversion options.

For more frequency conversion questions, visit our FAQ page or explore our conversion guides.

Helpful Conversion Guides

Learn more about unit conversion with our comprehensive guides:

๐Ÿ“š How to Convert Units

Step-by-step guide to unit conversion with practical examples.

๐Ÿ”ข Conversion Formulas

Essential formulas for frequency and other conversions.

โš–๏ธ Metric vs Imperial

Understand the differences between measurement systems.

โš ๏ธ Common Mistakes

Learn about frequent errors and how to avoid them.

View All Guides โ†’

All Frequency Conversions

Hertz to MillihertzHertz to KilohertzHertz to MegahertzHertz to GigahertzHertz to TerahertzHertz to Revolutions per MinuteHertz to Revolutions per SecondHertz to Beats per MinuteHertz to Cycles per SecondHertz to Radians per SecondMillihertz to HertzMillihertz to KilohertzMillihertz to MegahertzMillihertz to GigahertzMillihertz to TerahertzMillihertz to Revolutions per MinuteMillihertz to Revolutions per SecondMillihertz to Beats per MinuteMillihertz to Cycles per SecondMillihertz to Radians per SecondKilohertz to HertzKilohertz to MillihertzKilohertz to MegahertzKilohertz to GigahertzKilohertz to TerahertzKilohertz to Revolutions per MinuteKilohertz to Revolutions per SecondKilohertz to Beats per MinuteKilohertz to Cycles per SecondKilohertz to Radians per SecondMegahertz to HertzMegahertz to MillihertzMegahertz to KilohertzMegahertz to GigahertzMegahertz to TerahertzMegahertz to Revolutions per MinuteMegahertz to Revolutions per SecondMegahertz to Beats per MinuteMegahertz to Cycles per SecondMegahertz to Radians per SecondGigahertz to HertzGigahertz to MillihertzGigahertz to KilohertzGigahertz to MegahertzGigahertz to TerahertzGigahertz to Revolutions per MinuteGigahertz to Revolutions per SecondGigahertz to Beats per MinuteGigahertz to Cycles per SecondGigahertz to Radians per SecondTerahertz to HertzTerahertz to MillihertzTerahertz to KilohertzTerahertz to MegahertzTerahertz to GigahertzTerahertz to Revolutions per MinuteTerahertz to Revolutions per SecondTerahertz to Beats per MinuteTerahertz to Cycles per SecondTerahertz to Radians per SecondRevolutions per Minute to HertzRevolutions per Minute to MillihertzRevolutions per Minute to KilohertzRevolutions per Minute to MegahertzRevolutions per Minute to GigahertzRevolutions per Minute to TerahertzRevolutions per Minute to Revolutions per SecondRevolutions per Minute to Beats per MinuteRevolutions per Minute to Cycles per SecondRevolutions per Minute to Radians per SecondRevolutions per Second to HertzRevolutions per Second to MillihertzRevolutions per Second to KilohertzRevolutions per Second to MegahertzRevolutions per Second to GigahertzRevolutions per Second to TerahertzRevolutions per Second to Revolutions per MinuteRevolutions per Second to Beats per MinuteRevolutions per Second to Cycles per SecondRevolutions per Second to Radians per SecondBeats per Minute to HertzBeats per Minute to MillihertzBeats per Minute to KilohertzBeats per Minute to MegahertzBeats per Minute to GigahertzBeats per Minute to TerahertzBeats per Minute to Revolutions per MinuteBeats per Minute to Revolutions per SecondBeats per Minute to Cycles per SecondBeats per Minute to Radians per SecondCycles per Second to HertzCycles per Second to MillihertzCycles per Second to KilohertzCycles per Second to MegahertzCycles per Second to GigahertzCycles per Second to TerahertzCycles per Second to Revolutions per MinuteCycles per Second to Revolutions per SecondCycles per Second to Beats per MinuteRadians per Second to HertzRadians per Second to MillihertzRadians per Second to KilohertzRadians per Second to MegahertzRadians per Second to GigahertzRadians per Second to TerahertzRadians per Second to Revolutions per MinuteRadians per Second to Revolutions per SecondRadians per Second to Beats per MinuteRadians per Second to Cycles per Second

Other Frequency Units and Conversions

Explore other frequency units and their conversion options:

Verified Against Authority Standards

All conversion formulas have been verified against international standards and authoritative sources to ensure maximum accuracy and reliability.

NIST Reference on Constants, Units and Uncertainty

National Institute of Standards and Technology โ€” Fundamental physical constants and unit conversions

BIPM SI Units

Bureau International des Poids et Mesures โ€” International System of Units (SI) definitions and standards

ISO 80000

International Organization for Standardization โ€” Quantities and units international standards series

Last verified: December 3, 2025