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gigahertz to radians per second conversion

gigahertz to radians per second conversion table

gigahertz (GHz)radians per second (rad/s)
00
16283185307.1796
212566370614.359
318849555921.539
425132741228.718
531415926535.898
637699111843.078
743982297150.257
850265482457.437
956548667764.616
1062831853071.796
20125663706143.59
30188495559215.39
40251327412287.18
50314159265358.98
60376991118430.78
70439822971502.57
80502654824574.37
90565486677646.16
100628318530717.96
10006283185307179.6

How to convert gigahertz to radians per second?

To convert gigahertz (GHz) to radians per second (rad/s), we need to understand the relationship between these units.

1 gigahertz (1 GHz) is equal to 1 billion hertz (1 GHz = 10910^9 Hz).

Frequency in hertz (Hz) is related to angular frequency in radians per second (rad/s) by the formula: ω=2πf\omega = 2\pi f

Here, ω\omega is the angular frequency in radians per second, and ff is the frequency in hertz.

So, if we have 1 GHz, we can convert it to radians per second as follows: ω=2π×109 Hz\omega = 2\pi \times 10^9 \, \text{Hz} ω=2π×109 rad/s\omega = 2\pi \times 10^9 \, \text{rad/s} ω≈6.28×109 rad/s\omega \approx 6.28 \times 10^9 \, \text{rad/s}

So, 1 GHz is approximately 6.28×1096.28 \times 10^9 radians per second.

Real-World Examples of Other Quantities in Gigahertz

  1. Wi-Fi Frequencies:

    • Common Wi-Fi frequencies include 2.4 GHz and 5 GHz.
      • 2.4 GHz: ω=2π×2.4×109 Hz≈15.08×109 rad/s\omega = 2\pi \times 2.4 \times 10^9 \, \text{Hz} \approx 15.08 \times 10^9 \, \text{rad/s}
      • 5 GHz: ω=2π×5×109 Hz≈31.4×109 rad/s\omega = 2\pi \times 5 \times 10^9 \, \text{Hz} \approx 31.4 \times 10^9 \, \text{rad/s}

  2. Bluetooth Frequency:

    • Bluetooth typically operates in the 2.4 GHz range, similar to Wi-Fi.
      • 2.4 GHz: ω=2π×2.4×109 Hz≈15.08×109 rad/s\omega = 2\pi \times 2.4 \times 10^9 \, \text{Hz} \approx 15.08 \times 10^9 \, \text{rad/s}

  3. Cellular Networks:

    • 4G LTE bands can operate around 2.1 GHz:
      • 2.1 GHz: ω=2π×2.1×109 Hz≈13.2×109 rad/s\omega = 2\pi \times 2.1 \times 10^9 \, \text{Hz} \approx 13.2 \times 10^9 \, \text{rad/s}

  4. Microwave Ovens:

    • Microwave ovens typically operate at 2.45 GHz.
      • 2.45 GHz: ω=2π×2.45×109 Hz≈15.4×109 rad/s\omega = 2\pi \times 2.45 \times 10^9 \, \text{Hz} \approx 15.4 \times 10^9 \, \text{rad/s}

  5. FM Radio:

    • FM radio usually operates in the MHz range (0.1–0.3 GHz). For example, 100 MHz (0.1 GHz):
      • 0.1 GHz: ω=2π×0.1×109 Hz≈0.628×109 rad/s\omega = 2\pi \times 0.1 \times 10^9 \, \text{Hz} \approx 0.628 \times 10^9 \, \text{rad/s} ω≈628×106 rad/s\omega \approx 628 \times 10^6 \, \text{rad/s}

Summary of Common Frequencies and their Angular Frequencies:

  • 1 GHz: ≈6.28×109 rad/s\approx 6.28 \times 10^9 \, \text{rad/s}
  • 2.4 GHz: ≈15.08×109 rad/s\approx 15.08 \times 10^9 \, \text{rad/s}
  • 5 GHz: ≈31.4×109 rad/s\approx 31.4 \times 10^9 \, \text{rad/s}
  • 2.1 GHz: ≈13.2×109 rad/s\approx 13.2 \times 10^9 \, \text{rad/s}
  • 2.45 GHz: ≈15.4×109 rad/s\approx 15.4 \times 10^9 \, \text{rad/s}
  • 0.1 GHz (100 MHz): ≈628×106 rad/s\approx 628 \times 10^6 \, \text{rad/s}

These conversions help bridge the gap between how we usually think about frequencies (in hertz) and angular velocities (in radians per second), making it easier to understand phenomena in various domains like radio communication, wireless networking, and even household appliances.

See below section for step by step unit conversion with formulas and explanations. Please refer to the table below for a list of all the radians per second to other unit conversions.

What is gigahertz?

Gigahertz (GHz) is a unit of measurement for frequency, used to express the number of cycles or oscillations per second in electronic systems.

In essence, it represents one billion (1,000,000,000) cycles or oscillations per second. To break it down further:

  • 1 Hertz (Hz) = 1 cycle per second
  • 1 Kilohertz (kHz) = 1,000 cycles per second
  • 1 Megahertz (MHz) = 1 million cycles per second
  • 1 Gigahertz (GHz) = 1 billion cycles per second

In the context of electronic devices, such as computers, smartphones, and radios, gigahertz refers to the clock speed or operating frequency of a processor or other component. For example:

  • A computer with a CPU running at 2.5 GHz can execute 2.5 billion instructions per second.
  • A radio transmitter that operates on a frequency of 100 MHz would transmit 100 million cycles per second.

In summary, gigahertz is a unit of measurement for frequency, representing one billion cycles or oscillations per second, and is commonly used to express the operating frequencies of electronic devices.

What is radians per second?

The radians per second is a measurement used for defining angular velocity or rotational speed. This is the standard SI unit for measuring angular velocity. Unit of radians per second is rad/srad/s or rad∗s−1rad*s^{-1}.

1 rad∗s−1=1ω=3602πdeg∗s−1=12πHz=0.159155Hz1\ rad*s^{-1} = 1\omega = \frac{360}{2\pi} deg*s^{-1} = \frac{1}{2\pi} Hz = 0.159155 Hz

Wikipedia page for explanation on Radian per second

Complete gigahertz conversion table

Enter # of gigahertz
Convert 1 GHz to other unitsResult
gigahertz to millihertz (GHz to mHz)1000000000000
gigahertz to hertz (GHz to Hz)1000000000
gigahertz to kilohertz (GHz to kHz)1000000
gigahertz to megahertz (GHz to MHz)1000
gigahertz to terahertz (GHz to THz)0.001
gigahertz to rotations per minute (GHz to rpm)60000000000
gigahertz to degrees per second (GHz to deg/s)360000000000
gigahertz to radians per second (GHz to rad/s)6283185307.1796

Frequency conversions