Gigabytes per second to Gibibytes per hour conversion

How to convert gigabytes per second to gibibytes per hour?

Sure, let's go through the steps to convert 1 gigabyte per second (GB/s) to gibibytes per hour (GiB/h). We'll consider both the base 10 and base 2 conversions since they involve different definitions for gigabytes and gibibytes.

Base 10 (Decimal):

1 GB = $10^9$ bytes

Conversion steps:

1. Convert GB/s to bytes/s: $1 \text{ GB/s} = 1 \times 10^9 \text{ bytes/s}$

2. Convert bytes/s to bytes/hour: $1 \text{ byte/s} \times 3600 \text{ seconds/hour} = 3600 \text{ bytes/hour}$ $1 \times 10^9 \text{ bytes/s} \times 3600 = 3.6 \times 10^{12} \text{ bytes/hour}$

3. Convert bytes/hour to GiB/hour: 1 GiB = $2^{30}$ bytes $1 \text{ GiB} = 1,073,741,824 \text{ bytes}$ $3.6 \times 10^{12} \text{ bytes/hour} \div 1,073,741,824 \text{ bytes/GiB} \approx 3355.443 \text{ GiB/hour}$

Base 2 (Binary):

1 GiB = $2^{30}$ bytes

Conversion steps:

1. Convert GB (binary) to bytes: $1 \text{ GiB} = 2^{30} \text{ bytes}$ $1 \text{ GiB} = 1,073,741,824 \text{ bytes}$

2. Convert GiB/s to bytes/s: $1 \text{ GiB/s} = 1,073,741,824 \text{ bytes/s}$

3. Convert bytes/s to bytes/hour: $1,073,741,824 \text{ bytes/s} \times 3600 \text{ seconds/hour} = 3,863,661,158,400 \text{ bytes/hour}$

4. Convert bytes/hour to GiB/hour: $3,863,661,158,400 \text{ bytes/hour} \div 1,073,741,824 \text{ bytes/GiB} = 3600 \text{ GiB/hour}$

Summary:

• Using base 10: $1 \text{ GB/s} \approx 3355.443 \text{ GiB/hour}$

• Using base 2: $1 \text{ GiB/s} = 3600 \text{ GiB/hour}$

Real-world Examples of Data Transfer Rates:

1. USB 3.1 Gen 2 (10 Gbps):

   • 1.25 GB/s
   • $1.25 \text{ GB/s} \times 3600 \text{ seconds/hour} \approx 4,500 \text{ GB/hour}$

2. Ethernet (1 Gbps):

   • $1 Gbps \div 8 = 125 \text{ MB/s}$
   • $125 \text{ MB/s} \times 3600 \text{ seconds/hour} = 450,000 \text{ MB/hour}$
   • $450,000 \text{ MB/hour} \div 1024 = 439.45 \text{ GB/hour}$

3. PCIe 4.0 (x16, 256 Gbps):

   • $256 \text{ Gbps} \div 8 = 32 \text{ GB/s}$
   • $32 \text{ GB/s} \times 3600 \text{ seconds/hour} = 115,200 \text{ GB/hour}$

These examples show the importance of understanding how different units and data transfer rates translate into practical, real-world performance metrics.