Megabits per hour to Megabytes per second conversion

How to convert megabits per hour to megabytes per second?

To convert 1 Megabits per hour (Mbps) to Megabytes per second (MBps), you need to go through a series of unit conversions. Let's break it down step-by-step, and then differentiate between the base 10 (decimal) and base 2 (binary) standards.

Step-by-Step Conversion

1. Convert hours to seconds: There are 3600 seconds in an hour.

   $$\text{Time factor} = 1 \text{ hour} = 3600 \text{ seconds}$$

2. Convert Megabits to Megabytes: This depends on whether you're using base 10 or base 2.

   • Base 10 (Decimal): In the decimal system, 1 Megabit is 1,000,000 bits, and 1 Megabyte is 1,000,000 bytes. Therefore, the conversion factor between Megabits and Megabytes is:

     $$\text{1 Megabyte} = 1,000,000 \, \text{bytes} \times 8 \, \text{bits} = 8,000,000 \text{bits}$$

     So:

     $$\text{1 Megabit} = 1,000,000 \, \text{bits}$$

     $$\text{1 Megabyte} = \frac{1,000,000 \, \text{bytes}}{8} = 125,000 \, \text{bytes}$$

   • Base 2 (Binary): In the binary system, 1 Megabit is 1,048,576 bits (2^20 bits), and 1 Megabyte is 1,048,576 bytes (2^20 bytes). Therefore, the conversion factor between Megabits and Megabytes is:

     $$\text{1 Megabyte} = 1,048,576 \, \text{bytes} \times 8 \, \text{bits} = 8,388,608 \text{bits}$$

     So:

     $$\text{1 Megabit} = 1,048,576 \, \text{bits}$$

     $$\text{1 Megabyte} = \frac{1,048,576 \, \text{bytes}}{8} = 131,072 \, \text{bytes}$$

3. Combine the conversions:

   • Base 10:

     $$\text{1 Mbps} = \frac{1 \, \text{Megabit}}{3600 \, \text{seconds}} = \frac{1,000,000 \, \text{bits}}{3600 \, \text{seconds}} = \frac{1,000,000 \, \text{bits}}{8 \times 3600 \, \text{bytes}}$$

     $$= \frac{1,000,000}{28,800} \, \text{MBps} \approx 0.034722 \, \text{MBps}$$

   • Base 2:

     $$\text{1 Mbps} = \frac{1 \, \text{Megabit}}{3600 \, \text{seconds}} = \frac{1,048,576 \, \text{bits}}{3600 \, \text{seconds}} = \frac{1,048,576 \, \text{bits}}{8 \times 3600 \, \text{bytes}}$$

     $$= \frac{1,048,576}{28,800} \, \text{MBps} \approx 0.036458 \, \text{MBps}$$

Summary of Conversion:

• Base 10 (Decimal): 1 Mbps ≈ 0.034722 MBps

• Base 2 (Binary): 1 Mbps ≈ 0.036458 MBps

Real World Examples for Convert Quantities of Megabits per Hour

1. Streaming Video:

   • A standard definition (SD) video stream might use around 1 Mbps. Over an hour, you’d have:

     $$1 \, \text{Mbps} \times 3600 \, \text{seconds} = 3.6 \, \text{Gbps} = 450 \text{MB} \text{ (Base 10)}$$

     or:

     $$1.048576 \, \text{Mbps} \times 3600 \, \text{seconds} = 3.7748 \, \text{Gbps} = 471.68 \, \text{MB} \text{ (Base 2)}$$

2. File Downloads:

   • Downloading a large file at 50 Mbps:

     $$50 \, \text{Mbps} \times 3600 \, \text{seconds} = 180 \, \text{Gbps} = 22,500 \, \text{MB} \text{ (Base 10)}$$

     or:

     $$52.4288 \, \text{Mbps} \times 3600 \, \text{seconds} = 188.7397 \, \text{Gbps} = 23,592.08 \, \text{MB} \text{ (Base 2)}$$

3. Online Gaming:

   • If an online game typically uses around 5 Mbps:

     $$5 \, \text{Mbps} \times 3600 \, \text{seconds} = 18 \, \text{Gbps} = 2,250 \, \text{MB} \text{ (Base 10)}$$

     or:

     $$5.24288 \, \text{Mbps} \times 3600 \, \text{seconds} = 18.7748 \, \text{Gbps} = 2,359.20 \, \text{MB} \text{ (Base 2)}$$

These examples illustrate the amount of data that can be transferred or used over an hour at different Mbps rates in both base 10 and base 2 systems.