Gigabytes per hour to Tebibytes per month conversion

How to convert gigabytes per hour to tebibytes per month?

To convert data transfer rates from gigabytes per hour (GB/h) to tebibytes per month (TiB/month), we need to understand the conversion factors between these units and the time periods involved.

1. Understanding the units:

   • 1 Gigabyte (GB) in base 10 = 1,000,000,000 bytes.
   • 1 Tebibyte (TiB) in base 2 = 1,099,511,627,776 bytes (2^40 bytes).

2. Time conversion:

   • 1 hour = 60 minutes = 60 * 60 seconds = 3,600 seconds.
   • 1 day = 24 hours.
   • A month is typically considered to have approximately 30.44 days (average over a year).

Now we can calculate conversion both for base 10 and base 2.

Base 10 Conversion:

1. Calculate the number of seconds in a month: $1 \text{ month} = 30.44 \text{ days} \times 24 \text{ hours/day} \times 3600 \text{ seconds/hour} = 2,629,440 \text{ seconds}$

2. Convert Gigabytes per hour to Gigabytes per second: $1 \text{ GB/hour} = \frac{1 \text{ GB}}{3600 \text{ seconds}} \approx 0.00027778 \text{ GB/second}$

3. Convert to Gigabytes per month: $0.00027778 \text{ GB/second} \times 2,629,440 \text{ seconds} \approx 730 \text{ GB/month}$

4. Convert Gigabytes per month to Tebibytes per month: $\text{Since } 1 \text{ TiB} = 1,024 \text{ GB} \text{ (in base 10) ,}$ $\frac{730 \text{ GB/month}}{1,024} \approx 0.712 \text{ TiB/month}$

Base 2 Conversion:

1. Convert one GB to bytes and then to Tebibytes considering base 2 conversion:

   • 1 GB in base 2 = (1,000,000,000 bytes)
   • 1 TiB = 1,099,511,627,776 bytes.
   • 1 GB (base 10) to TiB (base 2) = $\frac{1,000,000,000}{1,099,511,627,776} \approx 0.000909 \text{ TiB/base 2 GB}$

2. Convert Gb/hour to TiB/month considering base 2: $1 \text{ GB/hour} = 0.000909 \text{ TiB/hour}$ $0.000909 \text{ TiB/hour} \times 24 \text{ hours/day} \times 30.44 \text{ days/month} \approx 0.663 \text{ TiB/month}$

Real-world Examples for Different Data Transfer Rates:

1. 5 GB/hour (Video Streaming Platform Data Usage):

   • Base 10: $0.00027778 \text{ GB/second} \times 5 \text{ GB/hour} = 0.0013889 \text{ GB/second}$ $0.0013889 \times 2,629,440 \text{ seconds/month} = 3,650 \text{ GB/month}$ $\frac{3,650 \text{ GB}}{1,024} \approx 3.56 \text{ TiB/month (base 10)}$
   • Base 2: $0.000909 \text{ TiB/hour} \times 5 = 0.004545 \text{ TiB/hour}$ $0.004545 \text{ TiB/hour} \times 24 \times 30.44 \approx 3.315 \text{ TiB/month (base 2)}$

2. 100 GB/hour (Large-Scale Data Transfer for Backup Systems):

   • Base 10: $0.00027778 \text{ GB/second} \times 100 \text{ GB/hour} = 0.027778 \text{ GB/second}$ $0.027778 \times 2,629,440 \text{ seconds/month} = 73,000 \text{ GB/month}$ $\frac{73,000 \text{ GB}}{1,024} \approx 71.29 \text{ TiB/month (base 10)}$
   • Base 2: $0.000909 \text{ TiB/hour} \times 100 = 0.0909 \text{ TiB/hour}$ $0.0909 \text{ TiB/hour} \times 24 \times 30.44 \approx 66.3 \text{ TiB/month (base 2)}$