Mebibits per second to Terabytes per hour conversion

How to convert mebibits per second to terabytes per hour?

To convert Mebibits per second (Mibps) to Terabytes per hour (TB/h), you have to go through a sequence of unit conversions. Here are the steps for both base 10 and base 2:

Base 2 (Common in computer science)

1. Understand the units:

   • 1 Mebibit (Mib) = 2^20 bits.
   • 1 Byte = 8 bits.
   • 1 Tebibyte (TiB) = 2^40 bytes.
   • 1 hour = 3600 seconds.

2. Steps to convert 1 Mibps to TiB/h:

   • First, convert Mibps to bits per second: $1 \; \text{Mibps} = 1 \times 2^{20} \; \text{bits/second}$
   • Then, convert bits per second to bytes per second: $1 \; \text{Mibps} = 1 \times (2^{20} \; \text{bits/second}) \times \frac{1\; \text{Byte}}{8\; \text{bits}}$
   • Then, convert bytes per second to bytes per hour: $1 \; \text{Mibps} = 1 \times \left( 2^{20} / 8 \right) \; \text{Bytes/second} \times 3600 \; \text{seconds/hour}$
   • Finally, convert bytes per hour to Tebibytes per hour (TiB/h): $1 \; \text{Mibps} = 1 \times \left( (2^{20} / 8) \times 3600 \right) \; \text{Bytes/hour} \times \frac{1 \; \text{TiB}}{2^{40} \; \text{Bytes}}$

   Simplifying: $1 \; \text{Mibps} = \frac{(2^{20} \times 3600)}{8 \times 2^{40}} \; \text{TiB/h}$ $1 \; \text{Mibps} \approx 0.000419 \; \text{TiB/h}$

Base 10 (Common in telecommunications)

1. Understand the units:

   • 1 Megabit (Mb) = 10^6 bits.
   • 1 Byte = 8 bits.
   • 1 Terabyte (TB) = 10^12 bytes.
   • 1 hour = 3600 seconds.

2. Steps to convert 1 Mbps to TB/h:

   • First, convert Mbps to bits per second: $1 \; \text{Mbps} = 1 \times 10^6 \; \text{bits/second}$
   • Then, convert bits per second to bytes per second: $1 \; \text{Mbps} = 1 \times (10^6 \; \text{bits/second}) \times \frac{1\; \text{Byte}}{8\; \text{bits}}$
   • Then, convert bytes per second to bytes per hour: $1 \; \text{Mbps} = 1 \times \left( 10^6 / 8 \right) \; \text{Bytes/second} \times 3600 \; \text{seconds/hour}$
   • Finally, convert bytes per hour to Terabytes per hour (TB/h): $1 \; \text{Mbps} = 1 \times \left( (10^6 / 8) \times 3600 \right) \; \text{Bytes/hour} \times \frac{1 \; \text{TB}}{10^{12} \; \text{Bytes}}$

   Simplifying: $1 \; \text{Mbps} = \frac{10^6 \times 3600}{8 \times 10^{12}} \; \text{TB/h}$ $1 \; \text{Mbps} = 0.00045 \; \text{TB/h}$

Real World Examples:

1. Real-time Online Gaming (~5-12 Mibps required):

   • Using 10 Mibps:
     • Base 2: $10 \times 0.000419 \approx 0.00419 \; \text{TiB/h}$
     • Base 10: $10 \times 0.00045 = 0.0045 \; \text{TB/h}$

2. Standard Definition Video Streaming (~3 Mibps required):

   • Using 3 Mibps:
     • Base 2: $3 \times 0.000419 \approx 0.001257 \; \text{TiB/h}$
     • Base 10: $3 \times 0.00045 = 0.00135 \; \text{TB/h}$

3. High Definition Video Streaming (~5 Mibps required):

   • Using 5 Mibps:
     • Base 2: $5 \times 0.000419 \approx 0.002095 \; \text{TiB/h}$
     • Base 10: $5 \times 0.00045 = 0.00225 \; \text{TB/h}$

4. 4K Video Streaming (~25 Mibps required):

   • Using 25 Mibps:
     • Base 2: $25 \times 0.000419 \approx 0.010475 \; \text{TiB/h}$
     • Base 10: $25 \times 0.00045 = 0.01125 \; \text{TB/h}$

These examples help illustrate how different Mibps rates convert into storage usage over time in both binary and decimal units.