Megabits per day to Terabytes per second conversion

How to convert megabits per day to terabytes per second?

Sure! Let’s go through the steps to convert 1 Megabit per day (Mbps) to Terabytes per second (TB/s) using both base 10 (decimal) and base 2 (binary) systems.

Base 10 (Decimal System)

1. Convert Megabits to Bits: 1 Megabit = $10^6$ bits (because "mega" in base 10 means $10^6$).

   So, 1 Megabit/day = $1 \times 10^6$ bits/day.

2. Convert Days to Seconds: 1 day = 24 hours = 24 × 60 minutes = 24 × 60 × 60 seconds = 86400 seconds.

3. Convert Bits/Day to Bits/Second: Bits per second = $\frac{10^6 \text{ bits}}{86400 \text{ seconds}}$.

   $\frac{10^6}{86400} \approx 11.574 \text{ bits/second}$

4. Convert Bits to Terabytes: 1 Terabyte = $10^{12}$ bytes (base 10), and 1 byte = 8 bits.

   So, 1 Terabyte = $10^{12} \times 8$ bits = $8 \times 10^{12}$ bits.

   Now, convert bits/second to Terabytes/second:

   $\text{TB/s} = \frac{11.574 \text{ bits/second}}{8 \times 10^{12} \text{ bits/Terabyte}}$

   $\approx 1.447 \times 10^{-12} \text{ TB/s}$

   $\approx 1.447 \text{ picoterabytes/second}$

Base 2 (Binary System)

1. Convert Megabits to Bits: 1 Megabit = $2^{20}$ bits (because "mega" in base 2 means $2^{20}$).

   So, 1 Megabit/day = $2^{20}$ bits/day = 1048576 bits/day.

2. Convert Days to Seconds: The number of seconds in a day remains the same: 86400 seconds.

3. Convert Bits/Day to Bits/Second: Bits per second = $\frac{1048576 \text{ bits}}{86400 \text{ seconds}}$.

   $\frac{1048576}{86400} \approx 12.135 \text{ bits/second}$

4. Convert Bits to Terabytes: 1 Terabyte = $2^{40}$ bytes (base 2), and 1 byte = 8 bits.

   So, 1 Terabyte = $2^{40} \times 8$ bits = $2^{43}$ bits.

   Now, convert bits/second to Terabytes/second:

   $\text{TB/s} = \frac{12.135 \text{ bits/second}}{2^{43} \text{ bits/Terabyte}}$

   $= \frac{12.135}{8 \times 2^{40}}$

   $\approx 1.375 \times 10^{-12} \text{ TB/s}$

   $\approx 1.375 \text{ picoterabytes/second}$

Real-World Examples of Megabits per Day

1. Internet Data Usage:

   • A residential user might consume around 3000 Megabits per day if they have moderate usage, which includes streaming videos, browsing, and occasional downloads.

2. Small Business Network:

   • A small office with 20 employees using internet-connected services might generate roughly 20000 Megabits per day.

3. Data Backup Systems:

   • A data backup service might transfer around 500000 Megabits per day while backing up files from numerous users or systems.

4. Streaming Services:

   • A single HD video stream typically consumes around 5000 Megabits per day based on an average bitrate of 5 Mbps and daily usage of watching ~2 hours of content.

By understanding these measurements and conversions, network administrators and data engineers can better plan for bandwidth requirements and data transfer capabilities in various applications and services.