Megabits per second to Gigabytes per hour conversion

How to convert megabits per second to gigabytes per hour?

Sure, let's walk through the conversion of 1 Megabit per second (Mbps) to Gigabytes per hour. There are subtle differences depending on whether you use base 10 (decimal) or base 2 (binary) units for Gigabytes, so I'll cover both.

Base 10 (Decimal) Conversion:

1. Determine the conversion factors:

   • 1 Megabit (Mb) = 1,000,000 bits (since "Mega" in base 10 is 10^6)
   • 1 byte = 8 bits
   • 1 Megabit per second (Mbps) = 1,000,000 bits per second
   • 1 Gigabyte (GB) = 1,000,000,000 bytes (since "Giga" in base 10 is 10^9)

2. Convert 1 Mbps to Megabytes per second (MBps):

   • $1 \text{ Mbps} = 1,000,000 \text{ bits per second}$
   • To convert to bytes per second: $1,000,000 \text{ bits per second} \div 8 = 125,000 \text{ bytes per second}$
   • To convert to Megabytes per second: $125,000 \text{ bytes per second} \div 1,000,000 = 0.125 \text{ MBps}$

3. Convert to Megabytes per hour:

   • $0.125 \text{ MBps} \times 60 \times 60 = 450 \text{ MB per hour}$

4. Convert to Gigabytes per hour:

   • $450 \text{ MB} \div 1,000 = 0.45 \text{ GB per hour}$

Base 2 (Binary) Conversion:

1. Determine the conversion factors:

   • 1 Megabit (Mb) = 1,048,576 bits (since "Mega" in base 2 is 2^20)
   • 1 byte = 8 bits
   • 1 Megabit per second (Mbps) = 1,048,576 bits per second
   • 1 Gigabyte (GiB) = 1,073,741,824 bytes (since "Giga" in base 2 is 2^30)

2. Convert 1 Mbps to Megabytes per second (MBps):

   • $1 \text{ Mbps} = 1,048,576 \text{ bits per second}$
   • To convert to bytes per second: $1,048,576 \text{ bits per second} \div 8 = 131,072 \text{ bytes per second}$
   • To convert to Megabytes per second: $131,072 \text{ bytes per second} \div 1,048,576 = 0.125 \text{ MBps}$

3. Convert to Megabytes per hour:

   • $0.125 \text{ MBps} \times 60 \times 60 = 450 \text{ MB per hour}$

4. Convert to Gigabytes per hour:

   • $450 \text{ MB} \div 1,024 = 0.439453125 \text{ GiB per hour}$

So summarizing:

• Base 10: 1 Mbps ≈ 0.45 GB per hour
• Base 2: 1 Mbps ≈ 0.439 GiB per hour

Real-World Examples for Other Quantities

• 10 Mbps:

  • Base 10: $10 \times 0.45 \text{ GB per hour} = 4.5 \text{ GB per hour}$
  • Base 2: $10 \times 0.439 \text{ GiB per hour} = 4.39 \text{ GiB per hour}$

• 100 Mbps:

  • Base 10: $100 \times 0.45 \text{ GB per hour} = 45 \text{ GB per hour}$
  • Base 2: $100 \times 0.439 \text{ GiB per hour} = 43.9 \text{ GiB per hour}$

• 1 Gbps (Gigabit per second):

  • Base 10: $1,000 \times 0.45 \text{ GB per hour} = 450 \text{ GB per hour}$
  • Base 2: $1,000 \times 0.439 \text{ GiB per hour} = 439 \text{ GiB per hour}$

These conversions are often used in networking to understand how most internet services, downloads, and data transfer rates can translate into storage usage over time.