Convert Hertz (Hz) to Radians Per Second (rad/s)
1 hertz equals 6.28319 radians per second.
Hertz to Radian Per Second Converter
How to Convert Hertz to Radian Per Second
1 hertz = 6.28319 radians per second
Radian Per Second = Hertz × 6.28319
Example: 1 Hz × 6.28319 = 6.28319 rad/s
Reverse Conversion
To convert radians per second back to hertz:
- Remember, 1 radian per second equals 0.159155 hertz.
- To convert 6.28319 rad/s to Hz, multiply
6.28319 x 0.159155, resulting in1 Hz.
Common Hertz to Radian Per Second Conversions
Hertz to radians per second Conversion Table
Reference table with common hertz to radians per second conversions. All values calculated with high precision.
Hertz to Radians Per Second Table
0.0001 to 12
Hertz to Radians Per Second Table
1 to 100000
Radians Per Second to Hertz Table
0.001 to 5
Radians Per Second to Hertz Table
10 to 1000000
Definition of Hertz
Hertz: The SI Unit of Frequency
The hertz (symbol: Hz) is the SI unit of frequency, defined as one cycle per second. It is named after Heinrich Rudolf Hertz, who first conclusively proved the existence of electromagnetic waves in 1887. One hertz means that an event repeats once per second.
Conversions to Other Units of Measurement:
- Kilohertz (kHz): 1 Hz equals 0.001 kHz. Kilohertz is commonly used for audio frequencies and AM radio broadcasting.
- Megahertz (MHz): 1 Hz equals 0.000001 MHz. Megahertz is used for FM radio and television broadcasting frequencies.
- Gigahertz (GHz): 1 Hz equals 10⁻⁹ GHz. Gigahertz is used for microwave frequencies, Wi-Fi, and modern processor clock speeds.
- Revolutions per Minute (rpm): 1 Hz equals 60 rpm. This conversion is fundamental in mechanical and electrical engineering for relating rotational speed to frequency.
- Radians per Second (rad/s): 1 Hz equals 2π rad/s (approximately 6.2832 rad/s). This angular frequency is essential in physics and signal processing.
The hertz is fundamental across science and engineering, from describing sound pitch and radio waves to processor clock speeds and power grid frequencies.
- Definition
- SI unit of frequency; one cycle (or event) per second. Symbol: Hz = s⁻¹
- Dimension
- T⁻¹ (inverse time)
- Common equivalents
- 1 Hz = 60 rpm (exact)
- 1 Hz = 2π rad/s ≈ 6.2832 rad/s
- 1 Hz = 0.001 kHz (exact)
- Sources
Definition of Radian Per Second
Radian per Second: Angular Frequency Unit
The radian per second (symbol: rad/s) is the SI unit of angular velocity and angular frequency. While hertz counts complete cycles, radians per second measures the rate of change of angular position. One complete cycle equals 2π radians, so the angular frequency ω (omega) relates to ordinary frequency f by ω = 2πf.
Conversions to Other Units of Measurement:
- Hertz (Hz): 1 rad/s equals 1/(2π) Hz (approximately 0.15915 Hz). To convert angular frequency to ordinary frequency, divide by 2π.
- Revolution per Minute (rpm): 1 rad/s equals 30/π rpm (approximately 9.5493 rpm). This conversion is essential for converting between physics notation and engineering notation.
- Revolution per Second (rps): 1 rad/s equals 1/(2π) rps (approximately 0.15915 rps).
Angular frequency is preferred in physics because it simplifies many equations. For example, the energy of a quantum is E = ℏω (where ℏ is the reduced Planck constant), and simple harmonic motion is described by x = A·sin(ωt).
- Definition
- SI unit of angular velocity; the rate of change of angular position in radians per second.
- Key relationship
- ω = 2πf (angular frequency = 2π × ordinary frequency)
- Common equivalents
- 1 rad/s = 1/(2π) Hz ≈ 0.15915 Hz
- 1 rad/s = 30/π rpm ≈ 9.5493 rpm
- 2π rad/s = 1 Hz (exact)
- Sources
About the Hertz
The hertz is named after Heinrich Hertz (1857-1894), who was the first to conclusively demonstrate the existence of electromagnetic waves predicted by James Clerk Maxwell's equations. Hertz's experiments in 1887 used a spark gap transmitter operating at about 50 MHz.
Power grids worldwide operate at either 50 Hz (Europe, Asia, Africa, most of South America) or 60 Hz (North America, parts of South America and Asia). This frequency determines the "hum" you sometimes hear from electrical equipment.
About the Radian Per Second
In electrical engineering, the angular frequency ω = 2πf simplifies many calculations. For a 50 Hz power grid, ω ≈ 314.16 rad/s; for 60 Hz, ω ≈ 376.99 rad/s. These values appear constantly in power system analysis, motor control, and signal processing.
Earth rotates at approximately 7.292 × 10⁻⁵ rad/s (one revolution per sidereal day of 23 hours, 56 minutes). This angular velocity is fundamental in calculating the Coriolis effect for weather patterns and long-range ballistics.
Frequently Asked Questions
How many radians per second are in one hertz?
One hertz equals 6.28319 radians per second. To convert, multiply the hertz value by 6.28319. For the reverse, divide the radian per second value by 6.28319 (or multiply by 0.159155).
What is 10 hertz in radians per second?
10 hertz = 62.832 radians per second. This is one of the most commonly searched conversions for this pair.
How precise is the hertz-to-radian per second conversion?
The factor 6.28319 is accurate to 6 significant figures, derived from international measurement standards. Our calculator uses full precision internally.
Looking for the reverse? Convert Radian Per Second to Hertz
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Related in other categories:
- Seconds to Minutes — Frequency = 1/period — hertz means cycles per second
- Radians to Degrees — Angular frequency: ω = 2πf
