Kilobits per day to Mebibytes per second conversion

How to convert kilobits per day to mebibytes per second?

To convert a data transfer rate from kilobits per day (kb/day) to mebibytes per second (MiB/s), it's important to recognize that you're converting between different units of time and different magnitudes of data:

Let's break the conversion down step by step for both base 10 and base 2:

Base 10 (Decimal)

First, understand the relationships between the units:

1 Kilobit (kb) = 1000 bits 1 Byte = 8 bits 1 Kilobyte (KB) = 1000 Bytes 1 Megabyte (MB) = 1000 Kilobytes 1 Mebibyte (MiB) = 1024 Kibibytes (KiB) 1 Kibibyte (KiB) = 1024 Bytes

1 day = 86400 seconds

Convert 1 kilobit per day to kilobits per second (kb/s):

$1 \text{ kb/day} = \frac{1 \text{ kb}}{86400 \text{ seconds}} = 1.1574 \times 10^{-5} \text{ kb/s}$

Convert kilobits per second to bits per second (b/s):

$1.1574 \times 10^{-5} \text{ kb/s} = 1.1574 \times 10^{-5} \times 1000 = 1.1574 \times 10^{-2} \text{ b/s}$

Convert bits per second to Bytes per second (B/s):

$1.1574 \times 10^{-2} \text{ b/s} = \frac{1.1574 \times 10^{-2}}{8} = 1.44675 \times 10^{-3} \text{ B/s}$

Convert Bytes per second to Kilobytes per second (KB/s):

$1.44675 \times 10^{-3} \text{ B/s} = \frac{1.44675 \times 10^{-3}}{1000} = 1.44675 \times 10^{-6} \text{ KB/s}$

Convert Kilobytes per second to Megabytes per second (MB/s):

$1.44675 \times 10^{-6} \text{ KB/s} = \frac{1.44675 \times 10^{-6}}{1000} = 1.44675 \times 10^{-9} \text{ MB/s}$

Since we need Mebibytes per second, we convert MB to MiB, noting that 1 MiB = 1.048576 MB:

$1.44675 \times 10^{-9} \text{ MB/s} = \frac{1.44675 \times 10^{-9} \text{ MB/s}}{1.048576} \approx 1.3798 \times 10^{-9} \text{ MiB/s}$

Base 2 (Binary)

1 Kilobit (kb) = 1024 bits 1 Byte = 8 bits 1 Kibibyte (KiB) = 1024 Bytes 1 Mebibyte (MiB) = 1024 Kibibytes (KiB) 1 day = 86400 seconds

Convert 1 kilobit per day to kilobits per second (kb/s):

$1 \text{ kb/day} = \frac{1 \text{ kb}}{86400 \text{ seconds}} = 1.1574 \times 10^{-5} \text{ kb/s}$

Convert kilobits per second to bits per second (b/s):

$1.1574 \times 10^{-5} \text{ kb/s} = 1.1574 \times 10^{-5} \times 1024 = 1.1859 \times 10^{-2} \text{ b/s}$

Convert bits per second to Bytes per second (B/s):

$1.1859 \times 10^{-2} \text{ b/s} = \frac{1.1859 \times 10^{-2}}{8} = 1.482375 \times 10^{-3} \text{ B/s}$

Convert Bytes per second to Kibibytes per second (KiB/s):

$1.482375 \times 10^{-3} \text{ B/s} = \frac{1.48237 \times 10^{-3}}{1024} = 1.447672 \times 10^{-6} \text{ KiB/s}$

Convert Kibibytes per second to Mebibytes per second (MiB/s):

$1.447672 \times 10^{-6} \text{ KiB/s} = \frac{1.447672 \times 10^{-6}}{1024} \approx 1.413679 \times 10^{-9} \text{ MiB/s}$

Real World Examples

• 10 Kilobits per day:

  • Base 10: $10 \times 1.3798 \times 10^{-9} = 1.3798 \times 10^{-8}$ MiB/s
  • Base 2: $10 \times 1.413679 \times 10^{-9} = 1.413679 \times 10^{-8}$ MiB/s

• 100 Kilobits per day:

  • Base 10: $100 \times 1.3798 \times 10^{-9} = 1.3798 \times 10^{-7}$ MiB/s
  • Base 2: $100 \times 1.413679 \times 10^{-9} = 1.413679 \times 10^{-7}$ MiB/s

• 1000 Kilobits per day:

  • Base 10: $1000 \times 1.3798 \times 10^{-9} = 1.3798 \times 10^{-6}$ MiB/s
  • Base 2: $1000 \times 1.413679 \times 10^{-9} = 1.413679 \times 10^{-6}$ MiB/s

These examples give you a sense of how these conversions would work across different magnitudes of data transfer rates.