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Radians per Second to Cycles per Second Converter

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

Quick Answer

1 Radians per Second = 0.159155 cps

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

Use the calculator below for instant, accurate conversions.

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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

Radians per Second to Cycles per Second Calculator

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

  1. Enter the value you want to convert in the 'From' field (Radians per Second).
  2. The converted value in Cycles 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.
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How to Convert Radians per Second to Cycles per Second: Step-by-Step Guide

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

Formula:

cps = rad/s ร— 0.159155

Example Calculation:

1 rad/s = 0.159155 cps

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

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๐Ÿ“‹ Unit Symbols

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What is a Radians per Second and a Cycles 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)

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

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

History of the Radians per Second and Cycles 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: rad/s vs cps

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

Common Uses for 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.

When to Use 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.

Additional Unit Information

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.

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†’

Conversion Table: Radians per Second to Cycles per Second

Radians per Second (rad/s)Cycles per Second (cps)
0.50.08
10.159
1.50.239
20.318
50.796
101.592
253.979
507.958
10015.916
25039.789
50079.578
1,000159.155

People Also Ask

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

To convert Radians per Second to Cycles per Second, enter the value in Radians 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 Radians per Second to Cycles per Second?

The conversion factor depends on the specific relationship between Radians per Second and Cycles 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 Cycles per Second back to Radians per Second?

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

Learn more โ†’

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

Radians per Second and Cycles 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.

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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

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Last verified: December 3, 2025