Megabits per day to Gibibytes per hour conversion

How to convert megabits per day to gibibytes per hour?

To convert from Megabits per day to Gibibytes per hour, you need to understand both the units involved and how to perform the conversions. Here's how you can do it.

1. Understand the Units:

   • Megabits (Mb): 1 Megabit = $10^6$ bits.
   • Gibibytes (GiB): 1 Gibibyte = $2^{30}$ bytes = 1,073,741,824 bytes.

2. Convert Megabits to Bits:

   • 1 Megabit per day = $1 \times 10^6$ bits per day.

3. Convert Days to Hours:

   • 1 day = 24 hours.

   • Therefore, 1 Megabit per day = $1 \times 10^6$ bits per 24 hours.

4. Convert Bits to Bytes:

   • 1 byte = 8 bits.
   • Therefore, $1 \times 10^6$ bits = $\frac{1 \times 10^6}{8}$ bytes = 125,000 bytes.

5. Convert Bytes per Day to Bytes per Hour:

   • There are 24 hours in a day.
   • Therefore, per hour = $\frac{125,000}{24}$ bytes = 5,208.33 bytes per hour.

6. Convert Bytes per Hour to Gibibytes per Hour:

   • 1 Gibibyte = $2^{30}$ bytes = 1,073,741,824 bytes.

   • Therefore, per hour in Gibibytes = $\frac{5,208.33}{1,073,741,824}$ GiB.

   • This yields: $\frac{5,208.33}{1,073,741,824} \approx 4.85 \times 10^{-6} GiB$

Base 10 Conversion (Gigabytes):

If you were to use base 10 for gigabytes (GB):

1. Gigabytes (GB): 1 Gigabyte = $10^9$ bytes.

2. Convert Bytes per Day to Bytes per Hour:

   • We already calculated $\frac{125,000}{24}$ bytes per hour = 5,208.33 bytes per hour.

3. Convert Bytes per Hour to Gigabytes per Hour:

   • 1 Gigabyte = $10^9$ bytes.

   • Therefore, per hour in Gigabytes = $\frac{5,208.33}{10^9}$.

   • This yields: $\frac{5,208.33}{10^9} \approx 5.21 \times 10^{-6} GB$

Therefore:

• 1 Megabit per day ≈ $4.85 \times 10^{-6}$ Gibibytes per hour (GiB/hour) (base 2)
• 1 Megabit per day ≈ $5.21 \times 10^{-6}$ Gigabytes per hour (GB/hour) (base 10)

Real World Examples for Other Quantities of Megabits per Day:

1. 10 Megabits per day:

   • Using similar steps, you would multiply the result for 1 Mb/day by 10.
   • Gibibytes/hour: $10 \times 4.85 \times 10^{-6} = 4.85 \times 10^{-5}$ GiB/hour.
   • Gigabytes/hour: $10 \times 5.21 \times 10^{-6} = 5.21 \times 10^{-5}$ GB/hour.

2. 1000 Megabits per day:

   • Gibibytes/hour: $1000 \times 4.85 \times 10^{-6} = 4.85 \times 10^{-3}$ GiB/hour.
   • Gigabytes/hour: $1000 \times 5.21 \times 10^{-6} = 5.21 \times 10^{-3}$ GB/hour.

3. 50 Megabits per day:

   • Gibibytes/hour: $50 \times 4.85 \times 10^{-6} = 2.425 \times 10^{-4}$ GiB/hour.
   • Gigabytes/hour: $50 \times 5.21 \times 10^{-6} = 2.605 \times 10^{-4}$ GB/hour.

By understanding these conversions, you can easily adapt to different quantities of data transfer rates and interpret them in terms of more commonly used units of data storage like Gigabytes (GB) or Gibibytes (GiB).