Hertz to Radians per Second

Hertz to Radians per Second Converter

Hertz to Radians per Second Conversion

Converting Hertz (Hz) to radians per second (rad/s) is common in physics, electrical engineering, signal processing, and rotational motion problems. This guide explains the relationship, formula, worked examples, and practical uses.

What Is Hertz (Hz)?

Hertz (Hz) measures frequency — the number of cycles that occur each second.

  • 1 Hz = 1 cycle per second
  • Used in waves, signals, and oscillations
  • Named after Heinrich Hertz

Examples:

  • AC power: 50 Hz or 60 Hz
  • Audio tones
  • Vibrations and oscillations

What Is Radians per Second (rad/s)?

Radians per second measures angular frequency — how fast something rotates in radians each second.

  • Used in rotational motion and wave equations
  • One full cycle equals 2π radians
  • Common symbol: ω (omega)

Key Relationship Between Hz and rad/s

The important concept:

One cycle = 2π radians

Since Hertz counts cycles per second, converting to radians per second requires multiplying by 2π.

Hertz to Radians per Second Formula

Radians per second = Hertz × 2π

Quick Formula

rad/s = Hz × 2π

Where:

  • π ≈ 3.14159
  • 2π ≈ 6.28318

Conversion Factor

Unit Equivalent
1 Hz 6.28318 rad/s
1 rad/s 0.159155 Hz

Step-by-Step Examples

Example 1: Convert 1 Hz to rad/s

1 × 2π = 6.28318 rad/s

Answer: ≈ 6.28 rad/s

Example 2: Convert 50 Hz to rad/s

50 × 2π = 314.159 rad/s

Answer: ≈ 314.16 rad/s

Example 3: Convert 60 Hz to rad/s

60 × 2π = 376.991 rad/s

Answer: ≈ 376.99 rad/s

Example 4: Convert 0.5 Hz to rad/s

0.5 × 2π = 3.14159 rad/s

Answer: ≈ 3.14 rad/s

Hz to rad/s Calculator (How to Use)

To convert quickly:

  1. Take the frequency in Hertz
  2. Multiply by 2π (≈ 6.28318)
  3. The result is in radians per second

Mental shortcut: Multiply Hz by 6.283.

Why Convert Hertz to Radians per Second?

This conversion is widely used in:

  • Physics wave equations
  • Simple harmonic motion
  • Electrical engineering
  • Control systems
  • Signal processing
  • Mechanical rotation analysis

Angular frequency (rad/s) is especially important when working with sine and cosine functions.

Common Search Questions

How many radians per second is 1 Hz?

1 Hz = 2π rad/s ≈ 6.283 rad/s

Why multiply Hz by 2π?

Because one full cycle equals 2π radians, and Hertz measures cycles per second.

Is rad/s the same as Hz?

No.

  • Hz measures cycles per second
  • rad/s measures angular speed
  • They are related but not equal

What is 100 Hz in radians per second?

100 × 2π = 628.318 rad/s

Answer: ≈ 628.32 rad/s

Reverse Conversion (rad/s to Hz)

To convert back:

Hertz = rad/s ÷ 2π

Example:

314.16 ÷ 2π ≈ 50 Hz

Final Thoughts

Converting Hertz to radians per second is straightforward once you remember the key rule:

Multiply by 2π (≈ 6.283).

This conversion is essential in physics, engineering, and signal analysis where angular frequency is required instead of standard frequency.