Megabits per second to Gibibits per hour conversion

How to convert megabits per second to gibibits per hour?

Converting 1 Megabit per second (Mbps) to Gibibits per hour (Gibibits/hour) requires understanding both the time conversion and the difference between base 10 (decimal) and base 2 (binary) units.

1. Conversion Factors:

   • 1 second (s) = 1/3600 hour (h)
   • Base 10: 1 Megabit (Mb) = 1,000,000 bits
   • Base 2: 1 Megabit (Mb) = 2^20 bits = 1,048,576 bits
   • 1 Gibibit (Gib) = 2^30 bits = 1,073,741,824 bits

2. Calculate the total number of bits transferred in one second:

   • In base 10: 1 Mbps = 1,000,000 bits per second
   • In base 2: 1 Mbps = 1,048,576 bits per second

3. Calculate the total number of bits transferred in one hour:

   • In base 10: $1,000,000 \text{ bits/second} \times 3,600 \text{ seconds/hour} = 3,600,000,000 \text{ bits/hour}$
   • In base 2: $1,048,576 \text{ bits/second} \times 3,600 \text{ seconds/hour} = 3,775,673,600 \text{ bits/hour}$

4. Convert the number of bits to Gibibits:

   • In base 10: $\frac{3,600,000,000 \text{ bits/hour}}{1,073,741,824 \text{ bits/Gibibit}} \approx 3.35 \text{ Gibibits/hour}$
   • In base 2: $\frac{3,775,673,600 \text{ bits/hour}}{1,073,741,824 \text{ bits/Gibibit}} \approx 3.52 \text{ Gibibits/hour}$

Thus, the conversions are:

• Base 10: 1 Mbps ≈ 3.35 Gibibits per hour
• Base 2: 1 Mbps ≈ 3.52 Gibibits per hour

Real-World Examples:

1. 5 Mbps broadband connection:

   • Base 10: 5 Mbps ≈ 5 × 3.35 ≈ 16.75 Gibibits per hour
   • Base 2: 5 Mbps ≈ 5 × 3.52 ≈ 17.6 Gibibits per hour

2. 100 Mbps fiber optic connection:

   • Base 10: 100 Mbps ≈ 100 × 3.35 ≈ 335 Gibibits per hour
   • Base 2: 100 Mbps ≈ 100 × 3.52 ≈ 352 Gibibits per hour

3. 1 Gbps (1,000 Mbps) high-speed business Internet:

   • Base 10: 1,000 Mbps ≈ 1,000 × 3.35 ≈ 3,350 Gibibits per hour
   • Base 2: 1,000 Mbps ≈ 1,000 × 3.52 ≈ 3,520 Gibibits per hour

4. 10 Mbps MPLS link:

   • Base 10: 10 Mbps ≈ 10 × 3.35 ≈ 33.5 Gibibits per hour
   • Base 2: 10 Mbps ≈ 10 × 3.52 ≈ 35.2 Gibibits per hour

By understanding these conversions, you can estimate the transfer speed and capacity for various internet and network connections more accurately, depending on whether the given speeds use base 10 or base 2 units.