Bytes per day to Mebibytes per second conversion

How to convert bytes per day to mebibytes per second?

To convert 1 Byte per day (B/day) to Mebibytes per second (MiB/s), you will need to understand the conversion factors between these units.

Base 2 (Binary System)

In the binary system, 1 Mebibyte (MiB) is defined as $2^{20}$ Bytes, or 1,048,576 Bytes.

1. Convert Days to Seconds:

   • 1 day = 24 hours/day × 60 minutes/hour × 60 seconds/minute = 86,400 seconds

2. Convert Bytes to Mebibytes:

   • 1 Byte = 1/2^{20} MiB

Combining these conversions: $1 \text{ B/day} \times \frac{1 \text{ day}}{86,400 \text{ seconds}} \times \frac{1 \text{ MiB}}{2^{20} \text{ Bytes}}$

$= \frac{1}{86,400 \times 2^{20}} \text{ MiB/s}$

$= \frac{1}{86,400 \times 1,048,576} \text{ MiB/s}$

$= \frac{1}{90,509,799,936} \text{ MiB/s}$

So: $1 \text{ Byte per day} = \approx 1.104 \times 10^{-11} \text{ MiB/s}$

Base 10 (Decimal System)

In the decimal system, 1 Megabyte (MB) is defined as $10^{6}$ Bytes.

1. Convert Days to Seconds:

   • Same as above: 1 day = 86,400 seconds

2. Convert Bytes to Megabytes:

   • 1 Byte = 1/10^{6} MB

Combining these conversions: $1 \text{ B/day} \times \frac{1 \text{ day}}{86,400 \text{ seconds}} \times \frac{1 \text{ MB}}{10^{6} \text{ Bytes}}$

$= \frac{1}{86,400 \times 10^{6}} \text{ MB/s}$

$= \frac{1}{86,400,000,000} \text{ MB/s}$

So: $1 \text{ Byte per day} = \approx 1.157 \times 10^{-11} \text{ MB/s}$

Real-World Examples of Bytes per Day

1. Typical Web Page Visit (500 KB)

   • 500 KB = 500 × 1,024 Bytes = 512,000 Bytes
   • Visits per day: 10 visits
   • Bytes per day: 10 × 512,000 = 5,120,000 Bytes/day

   For Base 2: $5,120,000 \text{ Bytes/day} = \approx \frac{5,120,000}{86,400 \times 1,048,576} \text{ MiB/s} \approx 5.92 \times 10^{-7} \text{ MiB/s}$

   For Base 10: $5,120,000 \text{ Bytes/day} = \approx \frac{5,120,000}{86,400 \times 10^6} \text{ MB/s} \approx 5.92 \times 10^{-8} \text{ MB/s}$

2. Simple IoT Device Upload (10 MB per day)

   • 10 MB = 10 × 10^6 Bytes = 10,000,000 Bytes/day

   For Base 2: $10,000,000 \text{ Bytes/day} = \approx \frac{10,000,000}{86,400 \times 1,048,576} \text{ MiB/s} \approx 1.14 \times 10^{-4} \text{ MiB/s}$

   For Base 10: $10,000,000 \text{ Bytes/day} = \approx \frac{10,000,000}{86,400 \times 10^6} \text{ MB/s} \approx 1.16 \times 10^{-4} \text{ MB/s}$

3. High Traffic Website (5 GB/day)

   • 5 GB = 5 × 10^9 Bytes = 5,000,000,000 Bytes/day

   For Base 2: $5,000,000,000 \text{ Bytes/day} = \approx \frac{5,000,000,000}{86,400 \times 1,048,576} \text{ MiB/s} \approx 5.68 \times 10^{-2} \text{ MiB/s}$

   For Base 10: $5,000,000,000 \text{ Bytes/day} = \approx \frac{5,000,000,000}{86,400 \times 10^6} \text{ MB/s} \approx 5.79 \times 10^{-2} \text{ MB/s}$