Mebibits per month to Terabytes per second conversion

How to convert mebibits per month to terabytes per second?

Converting 1 Mebibit per month to Terabytes per second involves several steps, as we need to account for both the time and the capacity units. Let's break this process down.

Base 2 Conversions

1. Convert Mebibits (Mibit) to Bits:

   • 1 Mebibit = $2^{20}$ bits = 1,048,576 bits

2. Convert Bits to Bytes (base 2):

   • 1 Byte = 8 bits
   • 1,048,576 bits / 8 = 131,072 Bytes

3. Convert Bytes to Tebibytes:

   • 1 Tebibyte (TiB) = $2^{40}$ Bytes = 1,099,511,627,776 Bytes
   • 131,072 Bytes to Tebibytes: $\frac{131,072}{1,099,511,627,776} \approx 1.1920929 \times 10^{-7}$ TiB

4. Convert Months to Seconds:

   • Assume an average month duration of 30.44 days (approximating the average length of a month considering leap years).
   • $30.44 \text{ days} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute}$
   • $30.44 \times 24 \times 60 \times 60 = 2,629,744$ seconds per month

5. Convert Terabytes (TB) to Tebibytes (TiB):

   • 1 Terabyte (TB) = $10^{12}$ Bytes = 1,000,000,000,000 Bytes

6. Convert Terabytes per Second:

   • $1.1920929 \times 10^{-7}$ TiB / 2,629,744 seconds
   • Convert TiB to TB: $1.1920929 \times 10^{-7}$ TiB = $1.1920929 \times 10^{-7} \times \frac{1,199,511,627,776}{10^{12}} = 1.287 \times 10^{-10}$
   • $\frac{1.287 \times 10^{-10} \text{ TB}}{2,629,744 \text{ seconds}}$
   • $\approx 4.89 \times 10^{-17} \text{ TB/s}$

Base 10 Conversions

1. Convert Mebibits (Mibit) to Bits:

   • 1 Mebibit = $2^{20}$ bits = 1,048,576 bits

2. Convert Bits to Bytes (base 10):

   • 1 Byte = 8 bits
   • 1,048,576 bits / 8 = 131,072 Bytes

3. Convert Bytes to Terabytes (TB):

   • 1 Terabyte (TB) = $10^{12}$ Bytes = 1,000,000,000,000 Bytes
   • 131,072 Bytes to Terabytes: $\frac{131,072}{1,000,000,000,000} = 1.31072 \times 10^{-7}$ TB

4. Convert Months to Seconds (same as above):

   • 2,629,744 seconds per month

5. Convert Terabytes per Second:

   • $1.31072 \times 10^{-7} \text{ TB} / 2,629,744 \text{ seconds}$
   • $\approx 4.99 \times 10^{-17} \text{ TB/s}$

Real World Examples

1. 100 Mib per month:

   • Base 2: $100 \times 4.89 \times 10^{-17} \approx 4.89 \times 10^{-15}$ TB/s
   • Base 10: $100 \times 4.99 \times 10^{-17} \approx 4.99 \times 10^{-15}$ TB/s

2. 1,000 Mib per month:

   • Base 2: $1000 \times 4.89 \times 10^{-17} \approx 4.89 \times 10^{-14}$ TB/s
   • Base 10: $1000 \times 4.99 \times 10^{-17} \approx 4.99 \times 10^{-14}$ TB/s

3. 1 Mibit per second (for comparison):

   • 1 Mib = $2^{20}$ bits/sec
   • $1,048,576$ bits/s = $1,048,576 / 8 / 10^{12} \approx 1.31 \times 10^{-7}$ TB/s (base 10)
   • $1,048,576 / 8 / 2^{40} \approx 1.19 \times 10^{-7}$ TiB/s (base 2)

Thus, 1 MebiBit per month translates to approximately $4.89 \times 10^{-17}$ Terabytes per second in base 2 and $4.99 \times 10^{-17}$ Terabytes per second in base 10.