Bytes per hour to Gigabytes per second conversion

How to convert bytes per hour to gigabytes per second?

To convert bytes per hour (B/h) to gigabytes per second (GB/s), you need to consider the following:

1. Number of seconds in an hour.
2. Conversion between bytes and gigabytes. Note that the conversion factor differs between base 10 (decimal) and base 2 (binary).

Base 10 (SI Units)

In base 10, 1 Gigabyte (GB) is defined as $1,000,000,000$ bytes.

1. There are 3600 seconds in an hour (60 seconds per minute * 60 minutes per hour).

So let's start the conversion:

1. Convert 1 byte per hour to bytes per second: $\frac{1 \text{ B}}{1 \text{ hr}} \times \frac{1 \text{ hr}}{3600 \text{ s}} = \frac{1}{3600} \text{ B/s}$

2. Convert bytes per second to gigabytes per second: $\frac{1}{3600} \text{ B/s} \times \frac{1 \text{ GB}}{1,000,000,000 \text{ B}} = \frac{1}{3600 \times 10^9} \text{ GB/s}$ $\approx 2.78 \times 10^{-13} \text{ GB/s}$

Base 2 (Binary Units)

In base 2, 1 Gibibyte (GiB) is defined as $1,073,741,824$ bytes.

1. There are still 3600 seconds in an hour.

Using the same steps:

1. Convert 1 byte per hour to bytes per second: $\frac{1 \text{ B}}{1 \text{ hr}} = \frac{1}{3600} \text{ B/s}$

2. Convert bytes per second to gibibytes per second: $\frac{1}{3600} \text{ B/s} \times \frac{1 \text{ GiB}}{1,073,741,824 \text{ B}} = \frac{1}{3600 \times 1,073,741,824} \text{ GiB/s}$ $\approx 2.58 \times 10^{-13} \text{ GiB/s}$

Real-World Examples

Let's consider some practical higher rates and use the same steps we used earlier:

Example 1: 10 Megabytes per hour (Base 10)

1 MB (base 10) = $1,000,000$ bytes.

1. Convert 10 MB per hour to bytes per second: $10 \times 1,000,000 \text{ B/hr} = 10,000,000 \text{ B/hr}$ $10,000,000 \text{ B/hr} \times \frac{1 \text{ hr}}{3600 \text{ s}} \approx 2777.78 \text{ B/s}$

2. Convert to gigabytes per second (base 10): $2777.78 \text{ B/s} \times \frac{1 \text{ GB}}{1,000,000,000 \text{ B}} \approx 2.78 \times 10^{-6} \text{ GB/s}$

Example 2: 5 Gibibytes per hour (Base 2)

1 GiB (base 2) = $1,073,741,824$ bytes.

1. Convert 5 GiB per hour to bytes per second: $5 \times 1,073,741,824 \text{ B/hr} = 5,368,709,120 \text{ B/hr}$ $5,368,709,120 \text{ B/hr} \times \frac{1 \text{ hr}}{3600 \text{ s}} \approx 1,491,307.53 \text{ B/s}$

2. Convert to gibibytes per second (base 2): $1,491,307.53 \text{ B/s} \times \frac{1 \text{ GiB}}{1,073,741,824 \text{ B}} \approx 1.39 \times 10^{-3} \text{ GiB/s}$

These conversions can be useful in understanding data transfer rates in contexts like network speeds, data storage requirements, and streaming services.