Megabits per hour to Terabits per second conversion

How to convert megabits per hour to terabits per second?

To convert megabits per hour (Mbps) to terabits per second (Tbps), you'll need to go through a series of unit conversions.

Base 10 Conversion

1. Conversion Factors:

   • 1 hour = 3600 seconds
   • 1 megabit (Mb) = $10^6$ bits
   • 1 terabit (Tb) = $10^{12}$ bits

2. Conversion Steps:

   • First, convert megabits to bits: $1 \, \text{Mb/h} = 1 \times 10^6 \, \text{bits/h}$
   • Next, convert hours to seconds: $1 \, \text{bit/h} = \frac{1 \, \text{bit}}{3600 \, \text{s}} \approx 2.7778 \times 10^{-4} \, \text{bits/s}$
   • Combine these conversions: $1 \, \text{Mb/h} = 10^6 \times 2.7778 \times 10^{-4} \, \text{bits/s} = 277.78 \, \text{bits/s}$
   • Finally, convert bits per second to terabits per second: $277.78 \, \text{bits/s} = 277.78 \times 10^{-12} \, \text{Tb/s} \approx 2.7778 \times 10^{-10} \, \text{Tb/s}$

Base 2 Conversion

1. Conversion Factors:

   • 1 hour = 3600 seconds
   • 1 megabit (Mb) = $2^{20}$ bits
   • 1 terabit (Tb) = $2^{40}$ bits

2. Conversion Steps:

   • First, convert megabits to bits: $1 \, \text{Mb/h} = 2^{20} \, \text{bits/h} = 1,048,576 \, \text{bits/h}$
   • Next, convert hours to seconds: $1 \, \text{bit/h} = \frac{1 \, \text{bit}}{3600 \, \text{s}} \approx 2.9104 \times 10^{-4} \, \text{bits/s}$
   • Combine these conversions: $1 \, \text{Mb/h} = 1,048,576 \times 2.9104 \times 10^{-4} \, \text{bits/s} = 305.23 \, \text{bits/s}$
   • Finally, convert bits per second to terabits per second: $305.23 \, \text{bits/s} = 305.23 \times 2^{-40} \approx 2.7715 \times 10^{-10} \, \text{Tb/s}$

Real World Examples

1. Streaming Video:

   • Medium-quality video streaming typically uses around 3 Mbps. Over an hour: $3 \, \text{Mbps} \times 1 \, \text{hour} = 3 \, \text{Mb/h}$ In terms of base 10: $3 \times 2.7778 \times 10^{-10} \, \text{Tb/s} \approx 8.3334 \times 10^{-10} \, \text{Tb/s}$ In terms of base 2: $3 \times 2.7715 \times 10^{-10} \, \text{Tb/s} \approx 8.3145 \times 10^{-10} \, \text{Tb/s}$

2. High-speed Download:

   • A high-speed internet connection might give you 200 Mbps. Over an hour: $200 \, \text{Mbps} \times 1 \, \text{hour} = 200 \, \text{Mb/h}$ In terms of base 10: $200 \times 2.7778 \times 10^{-10} \, \text{Tb/s} \approx 5.5556 \times 10^{-8} \, \text{Tb/s}$ In terms of base 2: $200 \times 2.7715 \times 10^{-10} \, \text{Tb/s} \approx 5.5430 \times 10^{-8} \, \text{Tb/s}$

3. Online Gaming:

   • Online gaming might use around 1 Mbps. Over an hour: $1 \, \text{Mbps} \times 1 \, \text{hour} = 1 \, \text{Mb/h}$ In terms of base 10: $1 \times 2.7778 \times 10^{-10} \, \text{Tb/s} \approx 2.7778 \times 10^{-10} \, \text{Tb/s}$ In terms of base 2: $1 \times 2.7715 \times 10^{-10} \, \text{Tb/s} \approx 2.7715 \times 10^{-10} \, \text{Tb/s}$

Thus, 1 megabit per hour converts to approximately $2.7778 \times 10^{-10}$ terabits per second in base 10 and $2.7715 \times 10^{-10}$ terabits per second in base 2. Different applications and data usages in real life can be calculated using these conversion principles.