Kilobits per second to Megabits per hour conversion

How to convert kilobits per second to megabits per hour?

To convert $1$ Kilobit per second ($\text{kbps}$) to Megabits per hour ($\text{Mbps}$), you need to understand the relationship between these units of measure and the time conversion.

Base 10 Conversion:

In the metric (base 10) system: 1 kilobit ($\text{kb}$) = 1,000 bits, 1 megabit ($\text{Mb}$) = 1,000,000 bits.

1 kilobit per second ($\text{kbps}$) can be converted to bits per second as follows: $1 \text{kbps} = 1,000 \text{bps}$

Since there are $3,600$ seconds in an hour: $1 \text{kbps} = 1,000 \text{bits per second} \times 3,600 \text{seconds}$ $1 \text{kbps} = 3,600,000 \text{bits per hour}$

Now convert bits to megabits: $1,000,000 \text{bits} = 1 \text{megabit}$ $3,600,000 \text{bits} = \frac{3,600,000}{1,000,000} \text{megabits}$ $3,600,000 \text{bits} = 3.6 \text{megabits}$

So, $1 \text{kbps} = 3.6 \text{Mbps per hour}$ in base 10.

Base 2 Conversion:

In the binary (base 2) system: 1 kilobit ($\text{kb}$) = 1,024 bits, 1 megabit ($\text{Mb}$) = 1,024 kilobits.

1 kilobit per second ($\text{kbps}$) in terms of bits per second: $1 \text{kbps} = 1,024 \text{bps}$

Again, considering there are $3,600$ seconds in an hour: $1 \text{kbps} = 1,024 \text{bits per second} \times 3,600 \text{seconds}$ $1 \text{kbps} = 3,686,400 \text{bits per hour}$

Convert bits to megabits (with 1 megabit = 1,048,576 bits): $1,048,576 \text{bits} = 1 \text{megabit}$ $3,686,400 \text{bits} = \frac{3,686,400}{1,048,576} \text{megabits}$ $3,686,400 \text{bits} \approx 3.515625 \text{megabits}$

So, $1 \text{kbps} \approx 3.515625 \text{Mbps per hour}$ in base 2.

Real-World Examples:

• If you have an internet connection speed of $128 \text{kbps}$:

  • In base 10: $128 \text{kbps} \times 3.6 \text{Mbps per kbps per hour} = 460.8 \text{Mbps per hour}$
  • In base 2: $128 \text{kbps} \times 3.515625 \text{Mbps per kbps per hour} = 450.0 \text{Mbps per hour}$

• A typical video streaming rate might be around $1,500 \text{kbps}$:

  • In base 10: $1,500 \text{kbps} \times 3.6 \text{Mbps per kbps per hour} = 5400 \text{Mbps per hour} = 5.4 \text{Gbps per hour}$
  • In base 2: $1,500 \text{kbps} \times 3.515625 \text{Mbps per kbps per hour} = 5273.4375 \text{Mbps per hour} = 5.2734375 \text{Gbps per hour}$

• A high-quality video conferencing rate may be around $3000 \text{kbps}$:

  • In base 10: $3000 \text{kbps} \times 3.6 \text{Mbps per kbps per hour} = 10,800 \text{Mbps per hour} = 10.8 \text{Gbps per hour}$
  • In base 2: $3000 \text{kbps} \times 3.515625 \text{Mbps per kbps per hour} = 10,546.875 \text{Mbps per hour} = 10.546875 \text{Gbps per hour}$