Megabits per hour to Gigabytes per second conversion

How to convert megabits per hour to gigabytes per second?

To convert 1 Megabit per hour (Mb/hr) to Gigabytes per second (GB/s), we need to understand the relationships between the units involved.

Conversion process

1. Convert Megabits to Bits:

   • $1 \text{ Megabit (Mb)} = 1,000,000 \text{ bits}$ (base 10)
   • $1 \text{ Megabit (Mb)} = 2^{20} \text{ bits} = 1,048,576 \text{ bits}$ (base 2)

2. Convert hours to seconds:

   • $1 \text{ hour} = 3,600 \text{ seconds}$

3. Combine and Convert:

   • For Base 10: $1 \text{ Megabit per hour} = \frac{1,000,000 \text{ bits}}{3,600 \text{ seconds}}$

   • For Base 2: $1 \text{ Megabit per hour} = \frac{1,048,576 \text{ bits}}{3,600 \text{ seconds}}$

4. Convert Bits per Second to Gigabytes per Second:

   • 1 Gigabyte (GB) = $10^9 \text{ bits}$ (base 10)
   • 1 Gibibyte (GiB) = $2^{30} \text{ bits} \approx 1,073,741,824 \text{ bits}$ (base 2)

   Therefore,

   • Base 10: $1 \text{ Megabit per hour} = \frac{1,000,000 \text{ bits}}{3,600 \text{ seconds} \times 10^9 \text{ bits/GB}}$
   • Base 2: $1 \text{ Megabit per hour} = \frac{1,048,576 \text{ bits}}{3,600 \text{ seconds} \times 1,073,741,824 \text{ bits/GiB}}$

Calculation

• For Base 10: $1 \text{ Mb/hr} = \frac{1,000,000}{3,600 \times 10^9} \text{ GB/s} = \frac{1,000,000}{3,600,000,000,000} \text{ GB/s} = 2.77778 \times 10^{-10} \text{ GB/s}$

• For Base 2: $1 \text{ Mb/hr} = \frac{1,048,576}{3,600 \times 1,073,741,824} \text{ GiB/s} = \frac{1,048,576}{3,864,170,574,400} \text{ GiB/s} = 2.71232 \times 10^{-10} \text{ GiB/s}$

Real-World Examples of Various Megabits per Hour Quantities

1. Streaming Quality:

   • A standard-definition (SD) video stream on Netflix might consume around 1,500 Kb/s, or 1.5 Mb/s: $1.5 \text{ Mb/s} \times 3600 \text{ s/hr} = 5,400 \text{ Mb/hr}$

2. File Downloads:

   • Downloading a large 10 GB file (80 Gb) over a connection that transfers data at 20 Mb/s: $20 \text{ Mb/s} \times 3,600 \text{ s/hr} = 72,000 \text{ Mb/hr}$

3. Internet Usage:

   • A standard web browsing usage consuming 2 Mb/s on average: $2 \text{ Mb/s} \times 3,600 \text{ s/hr} = 7,200 \text{ Mb/hr}$

4. High-Speed Downloads:

   • High-speed download on a fiber connection of 100 Mb/s: $100 \text{ Mb/s} \times 3,600 \text{ s/hr} = 360,000 \text{ Mb/hr}$

Note that these numbers illustrate how different data transfer rates translate into megabits per hour, and help show the relevance of the conversion in various real-world applications.