bits per hour to Terabits per second conversion

How to convert bits per hour to terabits per second?

To convert from bits per hour (bph) to Terabits per second (Tbps), you need to understand the relationship between these units and how to convert between them.

1. Conversion to base 10 (decimal): In base 10:

• 1 Terabit (Tb) = 10^12 bits
• 1 hour = 3600 seconds

So, starting with 1 bit per hour: $1 \, \text{bit/hour} = \frac{1 \, \text{bit}}{3600 \, \text{seconds}}$

Next, to convert bits to Terabits (Tb): $\frac{1 \, \text{bit}}{3600 \, \text{seconds}} \times \frac{1 \, \text{Tb}}{10^{12} \, \text{bits}} = \frac{1 \, \text{Tb}}{3600 \times 10^{12} \, \text{seconds}}$

Simplifying the denominator: $\frac{1 \, \text{Tb}}{3.6 \times 10^{15} \, \text{seconds}} = 2.78 \times 10^{-16} \, \text{Tbps}$

So 1 bit per hour is $2.78 \times 10^{-16}$ Terabits per second in base 10.

2. Conversion to base 2 (binary): In base 2:

• 1 Terabit (Tb) = 2^40 bits (this is less common for Terabits, as base 2 is usually more relevant for bytes)

Let’s perform a similar calculation: $1 \, \text{bit/hour} = \frac{1 \, \text{bit}}{3600 \, \text{seconds}}$

Next, to convert bits to Terabits (Tb) in base 2: $\frac{1 \, \text{bit}}{3600 \, \text{seconds}} \times \frac{1 \, \text{Tb}}{2^{40} \, \text{bits}} = \frac{1 \, \text{Tb}}{3600 \times 2^{40} \, \text{seconds}}$

Simplifying the denominator: $2^{40} \approx 1.1 \times 10^{12}$ $\frac{1 \, \text{Tb}}{3600 \times 1.1 \times 10^{12} \, \text{seconds}} = \frac{1 \, \text{Tb}}{3.96 \times 10^{15} \, \text{seconds}} \approx 2.53 \times 10^{-16} \, \text{Tbps}$

So 1 bit per hour is approximately $2.53 \times 10^{-16}$ Terabits per second in base 2.

Real-World Examples for Different Quantities of bits per hour:

1. 56 kbps (kilobits per second) Dial-up Internet: To find its equivalent in bits per hour: $56,000 \, \text{bps} \times 3600 \, \text{seconds/hour} = 2.016 \times 10^8 \, \text{bits per hour}$

2. 1 Mbps (Megabit per second) Broadband Internet: To find its equivalent in bits per hour: $1,000,000 \, \text{bps} \times 3600 \, \text{seconds/hour} = 3.6 \times 10^9 \, \text{bits per hour}$

3. 1 Gbps (Gigabit per second) High-speed Internet: To find its equivalent in bits per hour: $1,000,000,000 \, \text{bps} \times 3600 \, \text{seconds/hour} = 3.6 \times 10^{12} \, \text{bits per hour}$

By converting these amounts, you can see how typically smaller data transfer rates (when measured per hour) can still translate into notably larger quantities over time, giving context to various real-world data rates.