Mebibytes per second to Megabits per hour conversion

How to convert mebibytes per second to megabits per hour?

To convert 1 Mebibyte per second (MiB/s) to Megabits per hour (Mb/h), you need to understand the differences between the multiplies used in computing: base 2 (binary) and base 10 (decimal). Here's the detailed conversion process:

Base 2 (Binary)

1. Convert Mebibyte to Mebibit:

   • 1 Mebibyte (MiB) = $2^{20}$ bytes = 1,048,576 bytes
   • 1 byte = 8 bits, so: $1 \text{ MiB} = 1,048,576 \text{ bytes} \times 8 = 8,388,608 \text{ bits}$

2. Convert Mebibits per second to Megabits per second:

   • Since 1 Mebibit (Mibit) is equal to 1,048,576 bits and 1 Megabit (Mb) is equal to 1,000,000 bits (base 10), convert Mebibits to Megabits: $1 \text{ MiB/s} = \frac{8,388,608 \text{ bits/s}}{1,000,000 \text{ bits/Mb}} = 8.388608 \text{ Mb/s}$

3. Convert per second rate to per hour rate:

   • There are 3600 seconds in an hour: $8.388608 \text{ Mb/s} \times 3600 \text{ s/h} = 30,198.9888 \text{ Mb/h}$

Base 10 (Decimal)

1. Convert Mebibyte to Megabyte:

   • In base 10, 1 Megabyte (MB) = 1,000,000 bytes.
   • We are working with Mebibytes (MiB) here which we convert to bits directly: $1 \text{ MiB} = 1,048,576 \text{ bytes} \times 8 \text{ bits/byte} = 8,388,608 \text{ bits}$

2. Convert bits per second to Megabits per second:

   • 1 Megabit (Mb) = 1,000,000 bits (base 10), so: $1 \text{ MiB/s} = \frac{8,388,608 \text{ bits/s}}{1,000,000 \text{ bits/Mb}} = 8.388608 \text{ Mb/s}$

3. Convert per second rate to per hour rate:

   • There are 3600 seconds in an hour: $8.388608 \text{ Mb/s} \times 3600 \text{ s/h} = 30,198.9888 \text{ Mb/h}$

Summary for both bases

• The conversion from Mebibytes per second to Megabits per hour yields the same numerical value in both base 2 and base 10 once converted to bits and scaled properly—approximately 30,198.9888 Megabits per hour.

Real-world Examples of Data Rates

1. Residential Internet Speeds:

   • 100 MiB/s: High-speed fiber-optic internet connection. This would be about: $100 \text{ MiB/s} = 3,019,898.88 \text{ Mb/h}$

2. Corporate Network:

   • 10 MiB/s: A mid-range corporate network might have this rate. It would correspond to: $10 \text{ MiB/s} = 301,989.888 \text{ Mb/h}$

3. Streaming Services:

   • 5 MiB/s: A standard rate for streaming high-definition video. This would mean: $5 \text{ MiB/s} = 150,994.944 \text{ Mb/h}$

4. File Downloads:

   • 1 MiB/s: Downloading files from a reasonably fast server: $1 \text{ MiB/s} = 30,198.9888 \text{ Mb/h}$

Understanding these conversion principles enables you to translate data transfer rates into meaningful units, useful for various applications like internet speed comparison and data usage estimation.