Gigabits per month to Gibibytes per hour conversion

How to convert gigabits per month to gibibytes per hour?

To convert 1 Gigabit per month to Gibibytes per hour, you'll need to perform several steps, taking into account the number of seconds in a month, and the conversion factors for both base 10 (SI unit) and base 2 (binary unit).

Definitions:

1. Gigabit (Gb): In base 10, 1 Gigabit = $10^9$ bits.
2. Gibibyte (GiB): In base 2, 1 Gibibyte = $2^{30}$ bytes = $2^{30} \times 8$ bits = $2^{30+3}$ bits = $2^{33}$ bits.

Base 10 Calculation:

1. Convert Gigabits to bits: $1$ Gb = $10^9$ bits.

2. Determine the number of seconds in a month:

   • A month has an average of 30.44 days.
   • Seconds per month = $30.44 \times 24 \times 60 \times 60 = 2,629,744$ seconds.

3. Calculate bits per second: $\text{bits per second} = \frac{10^9 \text{ bits}}{2,629,744 \text{ seconds}}$

   $\approx 380.31 \text{ bits per second}$

4. Convert bits per second to Gibibytes per hour: $\text{bits per hour} = 380.31 \text{ bits/second} \times (60 \times 60)$ $\text{bits per hour} \approx 1,369,116 \text{ bits}$

   • Convert bits to Gibibytes: $\text{Gibibytes per hour} = \frac{1,369,116 \text{ bits}}{2^{33}}$

   $\approx 1,369,116 / 8,589,934,592$

   $\approx 0.0001596 \text{ GiB/hour}$

Base 2 Calculation:

1. Convert Gigabits to Gibibits:

   • Note that in base 2, the value is unchanged; 1 Gigabit is simply treated as a binary multiple.

2. Since 1 Gigabyte contains 8 Gibibytes:

   • $1 \text{Gb} = \frac{1}{8 \times 2^{30}} \text{ GiB}$
   • $1 \text{Gb} = \frac{1}{8 \times 1024^3}$
   • $1 \text{Gb} \approx 0.000125 \text{ GiB}$

3. Distribute this over seconds in a month and then convert to hours:

   • Plugging values here:

     $\text{Gibibytes per second} = \frac{10^9 \text{ bits}}{2,629,744 \times 8 \times 1024^3} \approx 4.812 \times 10^{-11} \text{ GiB/s}$

   • Multiply by $3600$ for per hour: $4.812 \times 10^{-11} \times 3600 \text{ GiB/hour} \approx 1.73232 \times 10^{-7} \text{ GiB/hour}$

Real-world Examples from Gigabits per month to Gibibytes per hour:

• 10 Gigabits per month:

  Base 10: $10 \times 0.0001596 \approx 0.001596 \text{ GiB/hour}$

  Base 2: $10 \times 1.73232 \times 10^{-7} \text{ GiB/hour}$ $\approx 1.732304 \times 10^{-6} \text{ GiB/hour}$

• 100 Gigabits per month:

  Base 10: $100 \times 0.0001596 \approx 0.01596 \text{ GiB/hour}$

  Base 2: $100 \times 1.73232 \times 10^{-7} \text{ GiB/hour}$ $\approx 1.73232 \times 10^{-5} \text{ GiB/hour}$

• 1000 Gigabits per month:

  Base 10: $1000 \times 0.0001596 \approx 0.1596 \text{ GiB/hour}$

  Base 2: $1000 \times 1.73232 \times 10^{-7} \text{ GiB/hour}$ $\approx 1.73232 \times 10^{-4} \text{ GiB/hour}$

This should give you a good idea of how to convert between these formats based on either base 10 or base 2 calculations.