Megabits per second to Gigabits per hour conversion

How to convert megabits per second to gigabits per hour?

To convert from Megabits per second (Mbps) to Gigabits per hour (Gb/hr), you need to understand the relationship between these units.

1 Megabit (Mb) = $1 \times 10^6$ bits (base 10) or $2^{20}$ bits (base 2). 1 Gigabit (Gb) = $1 \times 10^9$ bits (base 10) or $2^{30}$ bits (base 2). 1 hour = 3600 seconds.

Let's convert 1 Mbps to Gigabits per hour.

Base 10 Conversion:

1. Convert Mbps to Megabits per hour (Mb/hr): 1 Mbps = 1 Mb/sec. Therefore, in one hour (which is 3600 seconds): $1 \text{ Mbps} \times 3600 \text{ seconds} = 3600 \text{ Mb/hr}.$

2. Convert Megabits per hour to Gigabits per hour: 1 Gb = 1000 Mb (in base 10). $\frac{3600 \text{ Mb/hr}}{1000} = 3.6 \text{ Gb/hr}.$

So, in base 10, 1 Mbps is equivalent to 3.6 Gb/hr.

Base 2 Conversion:

1. Convert Mbps to Megabits per hour (Mb/hr): 1 Mbps remains the same in base 2. $1 \text{ Mbps} \times 3600 \text{ seconds} = 3600 \text{ Mb/hr}.$

2. Convert Megabits per hour to Gigabits per hour: 1 Gb = $2^{10}$ Mb = 1024 Mb (in base 2). $\frac{3600 \text{ Mb/hr}}{1024} \approx 3.515625 \text{ Gb/hr}.$

So, in base 2, 1 Mbps is approximately 3.515625 Gb/hr.

Real-World Examples:

Let's consider some other data rates:

10 Mbps

• Base 10: $\frac{10 \text{ Mbps} \times 3600}{1000} = 36 \text{ Gb/hr}.$
• Base 2: $\frac{10 \text{ Mbps} \times 3600}{1024} \approx 35.15625 \text{ Gb/hr}.$

100 Mbps

• Base 10: $\frac{100 \text{ Mbps} \times 3600}{1000} = 360 \text{ Gb/hr}.$
• Base 2: $\frac{100 \text{ Mbps} \times 3600}{1024} \approx 351.5625 \text{ Gb/hr}.$

1 Gbps to Megabits per hour

(Although rarely converted this way, this can be done for understanding):

• Base 10 (1 Gbps = 1000 Mbps): $1 \text{ Gbps} \times 3600 \text{ seconds} \times 1000 \text{ (to convert to Mb)} = 3,600,000 \text{ Mb/hr}.$

• Base 2 (1 Gbps = 1024 Mbps): $1 \text{ Gbps} \times 3600 \text{ seconds} \times 1024 \text{ (to convert to Mb)} = 3,686,400 \text{ Mb/hr}.$

In summary:

• 1 Mbps = 3.6 Gb/hr in base 10.
• 1 Mbps ≈ 3.515625 Gb/hr in base 2.

These conversions are essential in network calculations and data planning, especially when dealing with extensive data transfer over specific periods.