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Radians per Second to Hertz Converter

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

Quick Answer

1 Radians per Second = 0.159155 hertz

Formula: Radians per Second × conversion factor = Hertz

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: February 2026Reviewed by: Sam Mathew, Software Engineer

Radians per Second to Hertz Calculator

How to Use the Radians per Second to Hertz Calculator:

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

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

Formula:

Hz = rad/s × 0.159155

Example Calculation:

1 rad/s = 0.159155 Hz

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?

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What is a Radians per Second and a Hertz?

1 rad/s = 1 radian per second = 1/(2π) Hz ≈ 0.159155 Hz

Relationship to Hz:

  • ω (rad/s) = 2πf (Hz)
  • f (Hz) = ω/(2π) (rad/s)

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

1 Hz = 1 cycle per second = 1/second = s⁻¹

Metric prefixes:

  • 1,000 Hz = 1 kHz (kilohertz)
  • 1,000,000 Hz = 1 MHz (megahertz)
  • 1,000,000,000 Hz = 1 GHz (gigahertz)

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 Hertz belongs to the imperial/US customary system.

Common Uses and Applications: rad/s vs hertz

Explore the typical applications for both Radians per Second (imperial/US) and Hertz (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 hertz

AC Power: 50 Hz (Europe/Asia) or 60 Hz (Americas) - frequency of alternating current electricity. Audio: 20 Hz - 20,000 Hz (20 kHz) is the human hearing range. Display Refresh: Monitor and TV refresh rates (60 Hz, 120 Hz, 144 Hz, 240 Hz). Vibrations: Engine vibrations, seismic waves, mechanical oscillations measured in Hz.

Additional Unit Information

About Radians per Second (rad/s)

How do I convert rad/s to Hz?

Formula: Hz = rad/s ÷ (2π)

Examples:

  • 2π rad/s = 1 Hz
  • 6.28 rad/s ≈ 1 Hz
  • 377 rad/s = 60 Hz (US power frequency)
  • 314 rad/s = 50 Hz (European power frequency)

Reverse: rad/s = Hz × 2π

rad/s to Hz converter →

What is 2π rad/s?

2π rad/s = 1 Hz = 1 cycle per second

This is the key relationship:

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

Example:

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

How do I convert rad/s to RPM?

Formula: RPM = rad/s × (60/2π) ≈ rad/s × 9.549

Examples:

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

Reverse: rad/s = RPM × (2π/60) ≈ RPM × 0.1047

Derivation:

  • 1 revolution = 2π radians
  • 1 minute = 60 seconds
  • So: rad/s → rev/s → rev/min
  • rad/s × (1 rev / 2π rad) × (60 s / 1 min) = rad/s × 60/(2π) RPM

rad/s to RPM converter →

What is 377 rad/s?

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

Calculation: ω = 2πf = 2π × 60 ≈ 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(ωt) instead of x = A sin(2πft)
  • Direct angular displacement: θ = ωt
  • Natural for calculus: dx/dt, d²x/dt²

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

Conversion: 1 rad/s = 180/π deg/s ≈ 57.296 deg/s

Radians (rad/s):

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

Degrees (deg/s):

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

Example:

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

For engineering and physics calculations, use rad/s.

About Hertz (Hz)

How do I convert Hz to kHz?

Formula: kHz = Hz ÷ 1,000

Examples:

  • 1,000 Hz = 1 kHz
  • 440 Hz = 0.44 kHz (A4 musical note)
  • 20,000 Hz = 20 kHz (upper hearing limit)
  • 100 Hz = 0.1 kHz

Hz to kHz converter →

What is 60 Hz?

60 Hz is the AC power frequency in North America, parts of South America, and some Asian countries. The electricity alternates direction 60 times per second.

Also used for:

  • Standard monitor refresh rate (60 frames/second)
  • Fluorescent light flicker frequency
  • Basis for NTSC video standard

Countries using 60 Hz: USA, Canada, Mexico, Brazil, Japan (East), Saudi Arabia, Philippines, Taiwan

How many Hz can humans hear?

Human hearing range: 20 Hz - 20,000 Hz (20 kHz)

Age-dependent hearing:

  • Young children: 20 Hz - 20 kHz (full range)
  • Adults (25+): 20 Hz - 16 kHz
  • Adults (50+): 20 Hz - 12 kHz
  • Adults (70+): 20 Hz - 8 kHz

Sound categories:

  • Infrasound: <20 Hz (inaudible to humans)
  • Audible range: 20-20,000 Hz
  • Ultrasound: >20,000 Hz (inaudible to humans)

Speech range: 300-3,400 Hz (telephone bandwidth)

Hz to kHz converter →

Why is AC power 50 Hz or 60 Hz?

Historical reasons:

  • Early generators were designed for efficient transformer operation
  • 50/60 Hz prevents visible light flicker (persistence of vision)
  • Low enough for simple transformer design
  • High enough to prevent flicker

50 Hz vs 60 Hz:

  • 50 Hz: Slightly more efficient for power transmission
  • 60 Hz: Motors are slightly more compact and lighter
  • Both work well for incandescent lights, motors, and transformers

The split is historical - different pioneers chose different standards in the 1890s, and infrastructure locked in these frequencies.

How do I convert Hz to RPM?

Formula: RPM = Hz × 60

Examples:

  • 50 Hz = 3,000 RPM (synchronous motor speed at 50 Hz)
  • 60 Hz = 3,600 RPM (synchronous motor speed at 60 Hz)
  • 1 Hz = 60 RPM

Hz to RPM converter →

Conversion Table: Radians per Second to Hertz

Radians per Second (rad/s)Hertz (Hz)
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 Hertz?

To convert Radians per Second to Hertz, 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 →

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

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

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

Learn more →

What are common uses for Radians per Second and Hertz?

Radians per Second and Hertz 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

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📚 How to Convert Units

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🔢 Conversion Formulas

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⚠️ Common Mistakes

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All Frequency Conversions

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Other Frequency Units and Conversions

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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 — Fundamental physical constants and unit conversions

BIPM SI Units

Bureau International des Poids et Mesures — International System of Units (SI) definitions and standards

ISO 80000

International Organization for Standardization — Quantities and units international standards series

Last verified: February 19, 2026