Gigabits per hour to Tebibits per second conversion

How to convert gigabits per hour to tebibits per second?

To convert 1 Gigabit per hour (Gb/h) to Tebibits per second (Tibit/s), we need to understand the relationships between these units in both base 10 (decimal) and base 2 (binary) systems.

1. Conversion in base 10 (decimal):

   • 1 Gigabit (Gb) = $10^9$ bits
   • 1 hour = 3600 seconds

   Therefore, $1 \text{ Gb/h} = \frac{10^9 \text{ bits}}{3600 \text{ seconds}}$

   Simplifying this, $1 \text{ Gb/h} = \frac{10^9}{3600} \text{ bits per second}$ $1 \text{ Gb/h} \approx 2.78 \times 10^5 \text{ bits per second} (\text{bps})$

   Now, to convert bits per second to Tebibits per second:

   • 1 Tibibit (Tibit) = $2^{40}$ bits (approximately $1.0995 \times 10^{12}$ bits)

   Therefore, $2.78 \times 10^5 \text{ bps} = \frac{2.78 \times 10^5}{1.0995 \times 10^{12}} \text{ Tibit/s}$

   Simplifying, $\approx 2.53 \times 10^{-7} \text{ Tibit/s}$

2. Conversion in base 2 (binary):

   • 1 Gigabit (Gb) = $2^{30}$ bits (approximately 1.0737 billion bits)

   Therefore, $1 \text{ Gb/h (binary)} = \frac{2^{30}}{3600} \text{ bits per second}$

   Simplifying this, $1 \text{ Gb/h (binary)} \approx 298,261 \text{ bits per second}$

   Now, to convert bits per second to Tebibits per second:

   • 1 Tebibit (Tibit) = $2^{40}$ bits

   Therefore, $298,261 \text{ bps} = \frac{298,261}{2^{40}} \text{ Tibit/s} = \frac{298,261}{1,099,511,627,776} \text{ Tibit/s}$

   Simplifying, $\approx 2.71 \times 10^{-7} \text{ Tibit/s}$

Real-World Examples for Other Quantities of Gigabits per Hour

• Home Internet Speed:

  • If your home internet speed is 100 Mbps (Megabits per second), in an hour, you would transfer: $100 \text{ Mbps} \times 3600 \text{ seconds} = 360,000 \text{ Megabits per hour} = 360 \text{ Gigabits per hour}$

• Data Center Network:

  • A data center might use a 1 Tbps (Terabit per second) link. In an hour, this would be: $1 \text{ Tbps} \times 3600 \text{ seconds} = 3,600 \text{ Terabits per hour} = 3,600,000 \text{ Gigabits per hour}$

• Streaming Service:

  • A 4K video stream might use 25 Mbps. Over an hour: $25 \text{ Mbps} \times 3600 \text{ seconds} = 90,000 \text{ Megabits per hour} = 90 \text{ Gigabits per hour}$

These examples highlight how data rates scale up depending on the applications, from home internet connections to data center operations and streaming services.