Cycles per Second to Radians per Second Converter

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.