Kilobits per hour to Gigabytes per second conversion

How to convert kilobits per hour to gigabytes per second?

To convert 1 kilobit per hour (kb/hr) to gigabytes per second (GB/s), we need to perform several steps, converting from kilobits to bits, then to seconds, and finally from bits to gigabytes. I'll show you both base-10 (decimal) and base-2 (binary) conversions.

Base-10 (Decimal) Conversion

1. Convert kilobits to bits:

   • $1 \text{ kilobit} = 1,000 \text{ bits}$ So, $1 \text{ kb/hr} = 1,000 \text{ bits/hr}$.

2. Convert hours to seconds:

   • $1 \text{ hour} = 3,600 \text{ seconds}$ So, $1,000 \text{ bits/hr} = \frac{1,000 \text{ bits}}{3,600 \text{ seconds}}$.

3. Calculate bits per second:

   • $\frac{1,000}{3,600} \text{ bits/second} ≈ 0.27778 \text{ bits/second}$

4. Convert bits to bytes:

   • $1 \text{ byte} = 8 \text{ bits}$ So, $\frac{0.27778 \text{ bits/second}}{8} ≈ 0.03472 \text{ bytes/second}$.

5. Convert bytes to gigabytes:

   • $1 \text{ gigabyte} = 10^9 \text{ bytes}$ So, $\frac{0.03472 \text{ bytes/second}}{10^9} = 3.472 \times 10^{-11} \text{ GB/second}$.

Base-2 (Binary) Conversion

1. Convert kilobits to bits:

   • $1 \text{ kilobit} = 1,024 \text{ bits}$ So, $1 \text{ kb/hr} = 1,024 \text{ bits/hr}$.

2. Convert hours to seconds:

   • $1 \text{ hour} = 3,600 \text{ seconds}$ So, $1,024 \text{ bits/hr} = \frac{1,024 \text{ bits}}{3,600 \text{ seconds}}$.

3. Calculate bits per second:

   • $\frac{1,024}{3,600} \text{ bits/second} ≈ 0.28444 \text{ bits/second}$.

4. Convert bits to bytes:

   • $1 \text{ byte} = 8 \text{ bits}$ So, $\frac{0.28444 \text{ bits/second}}{8} ≈ 0.03556 \text{ bytes/second}$.

5. Convert bytes to gigabytes:

   • $1 \text{ gigabyte} = 2^{30} \text{ bytes} = 1,073,741,824 \text{ bytes}$ So, $\frac{0.03556 \text{ bytes/second}}{1,073,741,824} ≈ 3.313 \times 10^{-11} \text{ GB/second}$.

Real World Examples for Kilobits per Hour

• Low-quality streaming audio: Around 128 kbps is 460,800 kb/hour, which equates to approximately 4.6 x 10^{-4} GB/s (base-10) or 4.29 x 10^{-4} GB/s (base-2).

• Dial-up Internet speeds: Old dial-up connections a decade ago typically delivered around 56 kbps, which is roughly 201,600 kb/hour, equating to roughly 2.0 x 10^{-4} GB/s (base-10) or 1.88 x 10^{-4} GB/s (base-2).

• Low bandwidth IoT devices: Consider a simple sensor transmitting data intermittently, with an average rate of 10 kb/hour, equating to about 2.78 x 10^{-10} GB/s (base-10) or 2.66 x 10^{-10} GB/s (base-2).

These examples help to contextualize the scale of data transfer rates for different use cases.