bits per second to Gigabytes per month conversion

How to convert bits per second to gigabytes per month?

To convert a data transfer rate from bits per second (bps) to Gigabytes per month, you need to follow several steps:

1. Convert bits per second to bits per minute: $\text{bits per minute} = \text{bps} \times 60$

2. Convert bits per minute to bits per hour: $\text{bits per hour} = \text{bits per minute} \times 60$

3. Convert bits per hour to bits per day: $\text{bits per day} = \text{bits per hour} \times 24$

4. Convert bits per day to bits per month (assuming 30 days in a month): $\text{bits per month} = \text{bits per day} \times 30$

5. Convert bits per month to bytes per month (1 byte = 8 bits): $\text{bytes per month} = \frac{\text{bits per month}}{8}$

6. Convert bytes per month to Gigabytes per month: $\text{Gigabytes per month} = \frac{\text{bytes per month}}{10^9} \quad \text{(base 10)}$ $\text{Gigabytes per month} = \frac{\text{bytes per month}}{2^{30}} \quad \text{(base 2)}$

For 1 bit per second, the calculations are as follows:

Base 10 Calculation:

1. Bits per minute: $1 \text{ bps} \times 60 = 60 \text{ bits per minute}$

2. Bits per hour: $60 \text{ bits per minute} \times 60 = 3,600 \text{ bits per hour}$

3. Bits per day: $3,600 \text{ bits per hour} \times 24 = 86,400 \text{ bits per day}$

4. Bits per month: $86,400 \text{ bits per day} \times 30 = 2,592,000 \text{ bits per month}$

5. Bytes per month: $\frac{2,592,000 \text{ bits per month}}{8} = 324,000 \text{ bytes per month}$

6. Gigabytes per month (base 10): $\frac{324,000 \text{ bytes per month}}{10^9} = 0.000000324 \text{ GB per month}$

Base 2 Calculation:

1. Steps 1-5 are identical.

2. Gigabytes per month (base 2): $\frac{324,000 \text{ bytes per month}}{2^{30}} = \frac{324,000}{1,073,741,824} \approx 0.000000301 \text{ GB per month}$

Real World Examples:

1. 10 Mbps Internet Connection:

   • Base 10: $10 \times 0.000000324 = 0.00000324 \text{ GB/s} \\ 0.00000324 \text{ GB/s} \times 60 \times 60 \times 24 \times 30 = 8.64 \text{ GB/month}$
   • Base 2: $10 \times 0.000000301 = 0.00000301 \text{ GB/s} \\ 0.00000301 \text{ GB/s} \times 60 \times 60 \times 24 \times 30 \approx 7.78 \text{ GB/month}$

2. 100 Mbps Internet Connection:

   • Base 10: $100 \times 0.000000324 = 0.0000324 \text{ GB/s} \\ 0.0000324 \text{ GB/s} \times 60 \times 60 \times 24 \times 30 = 86.4 \text{ GB/month}$
   • Base 2: $100 \times 0.000000301 = 0.0000301 \text{ GB/s} \\ 0.0000301 \text{ GB/s} \times 60 \times 60 \times 24 \times 30 \approx 77.8 \text{ GB/month}$

3. 1 Gbps (Gigabit per second) Connection:

   • Base 10: $1000 \times 0.000000324 = 0.000324 \text{ GB/s} \\ 0.000324 \text{ GB/s} \times 60 \times 60 \times 24 \times 30 = 864 \text{ GB/month}$
   • Base 2: $1000 \times 0.000000301 = 0.000301 \text{ GB/s} \\ 0.000301 \text{ GB/s} \times 60 \times 60 \times 24 \times 30 \approx 777.6 \text{ GB/month}$

These examples illustrate the significant difference between base 10 and base 2 calculations, especially as the data rates increase.