Gigabits per second to Terabits per hour conversion

How to convert gigabits per second to terabits per hour?

Certainly! Let's start by converting 1 Gigabit per second (Gbps) to Terabits per hour (Tbph).

Base 10 (Decimal)

In the base 10 system:

• 1 Gigabit (Gb) = $10^9$ bits
• 1 Terabit (Tb) = $10^{12}$ bits

Step-by-step conversion:

1. Convert seconds to hours:

   There are 3600 seconds in one hour.

   So, $1 \text{ Gbps} = \frac{10^9 \text{ bits}}{1 \text{ second}} \times 3600 \text{ seconds}$ in an hour.

2. Calculate the bits per hour:

   $1 \text{ Gbps} \times 3600 = 3.6 \times 10^{12} \text{ bits}$ per hour.

3. Convert bits to Terabits:

   $\frac{3.6 \times 10^{12} \text{ bits}}{10^{12} \text{ bits per Terabit}} = 3.6 \text{ Tb}$

So, 1 Gbps = 3.6 Terabits per hour (Tbph) in base 10.

Base 2 (Binary)

In the base 2 system:

• 1 Gigabit (Gb) = $2^{30}$ bits (also known as a Gibibit)
• 1 Terabit (Tb) = $2^{40}$ bits (also known as a Tebibit)

Step-by-step conversion:

1. Convert seconds to hours:

   There are 3600 seconds in one hour.

   So, $1 \text{ Gbps} = \frac{2^{30} \text{ bits}}{1 \text{ second}} \times 3600 \text{ seconds}$ in an hour.

2. Calculate bits per hour:

   $2^{30} \text{ bits} \times 3600 = 2^{30} \times 3600$ bits per hour.

   $2^{30} \text{ bits} = 1,073,741,824 \text{ bits}$, so:

   $1,073,741,824 \text{ bits} \times 3600 = 3,865,048,473,600 \text{ bits}$

3. Convert bits to Terabits:

   $\frac{3,865,048,473,600 \text{ bits}}{2^{40} \text{ bits per Tebibit}}$

   Since $2^{40} = 1,099,511,627,776$:

   $\frac{3,865,048,473,600}{1,099,511,627,776} \approx 3.516 \text{ Tebibits}$

So, 1 Gbps ≈ 3.516 Tebibits per hour (Tbph) in base 2.

Real-World Examples for Other Rates in Gbps

1. 5 Gbps USB 3.0:

   • In base 10: $5 \times 3.6 = 18$ Terabits per hour.
   • In base 2: $5 \times 3.516 = 17.58$ Tebibits per hour.

2. 10 Gbps Ethernet:

   • In base 10: $10 \times 3.6 = 36$ Terabits per hour.
   • In base 2: $10 \times 3.516 = 35.16$ Tebibits per hour.

3. 40 Gbps Infiniband:

   • In base 10: $40 \times 3.6 = 144$ Terabits per hour.
   • In base 2: $40 \times 3.516 = 140.64$ Tebibits per hour.

These conversions provide insight into how much data can be transferred over various high-speed connections, useful in networking, data centers, and big data applications.