bits per second to Gibibits per month conversion

How to convert bits per second to gibibits per month?

To convert bits per second (bps) to Gibibits per month, we need to consider both the time units involved (seconds to months) and the data size units (bits to Gibibits).

Converting bps to Gibibits per month

1. Start with the conversion factors:

   • Seconds in a month: We'll consider 30 days in a month for approximation. $30 \text{ days} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 2,592,000 \text{ seconds/month}$

2. Convert bits to Gibibits:

   • Using base 2, 1 Gibibit (Gibit) = $2^{30}$ bits.
   • Using base 10, 1 Gigabit (Gb) = $10^9$ bits.

Base 2 (Gibibits)

• Calculation: $\text{bps} \times \text{seconds per month} \div 2^{30} = \frac{1 \text{ bps} \times 2,592,000 \text{ seconds/month}}{2^{30} \text{ bits/Gibit}}$

• Perform the division: $\frac{2,592,000}{2^{30}} \approx \frac{2,592,000}{1,073,741,824} \approx 0.002415 \text{ Gibits/month}$

Base 10 (Gigabits)

• Calculation: $\text{bps} \times \text{seconds per month} \div 10^9 = \frac{1 \text{ bps} \times 2,592,000 \text{ seconds/month}}{10^9 \text{ bits/Gb}}$

• Perform the division: $\frac{2,592,000}{10^9} = 0.002592 \text{ Gb/month}$

Summary

• Base 2 (Gibibits): 1 bps = 0.002415 Gibibits per month
• Base 10 (Gigabits): 1 bps = 0.002592 Gigabits per month

Real-World Examples

1. 10 Mbps Internet Connection:

   • Base 2: $10,000,000 \text{ bps} \times \frac{2,592,000}{2^{30}} \approx 24.15 \text{ Gibits/month}$
   • Base 10: $10,000,000 \text{ bps} \times \frac{2,592,000}{10^9} = 25.92 \text{ Gb/month}$

2. 1 Gbps Fiber-optic Connection:

   • Base 2: $1,000,000,000 \text{ bps} \times \frac{2,592,000}{2^{30}} \approx 2,415 \text{ Gibits/month}$
   • Base 10: $1,000,000,000 \text{ bps} \times \frac{2,592,000}{10^9} = 2,592 \text{ Gb/month}$

3. 5 Gbps Data Transfer Rate:

   • Base 2: $5,000,000,000 \text{ bps} \times \frac{2,592,000}{2^{30}} \approx 12,075 \text{ Gibits/month}$
   • Base 10: $5,000,000,000 \text{ bps} \times \frac{2,592,000}{10^9} = 12,960 \text{ Gb/month}$

These real-world examples show how different data rates would translate into monthly data usage measured in Gibibits or Gigabits.