Megabits per day to Tebibits per second conversion

How to convert megabits per day to tebibits per second?

To convert from Megabits per day (Mb/day) to Tebibits per second (Tibit/s), you need to consider the following steps and units. It is essential to distinguish between base 10 (decimal) and base 2 (binary) systems, as they yield different results. Let's explain both:

Base 10 (Decimal System)

1. Megabits to bits: $1 \text{ Megabit} = 10^6 \text{ bits}$

2. Day to seconds: $1 \text{ day} = 24 \times 60 \times 60 = 86400 \text{ seconds}$

3. Combining the conversion: $\frac{1 \text{ Megabit/day}}{\text{seconds}} = \frac{10^6 \text{ bits}}{86400 \text{ seconds}} = \frac{10^6}{86400} \text{ bits/second}$

4. Tebibits in base 10: $1 \text{ Tebibit} (base 10) = 10^{12} \text{ bits}$

5. Putting it all together: $\frac{10^6 \text{ bits}}{86400 \text{ seconds} \times 10^{12}} \text{ Tebibits/second} = \frac{10^6}{86400 \times 10^{12}} \text{ Tibit/s} = \frac{1}{86400 \times 10^6} \text{ Tibit/s} = 1.157407 \times 10^{-11} \text{ Tibit/s}$

Base 2 (Binary System)

1. Megabits to bits: $1 \text{ Megabit} = 2^{20} \text{ bits}$

2. Day to seconds: $1 \text{ day} = 24 \times 60 \times 60 = 86400 \text{ seconds}$

3. Combining the conversion: $\frac{1 \text{ Megabit/day}}{\text{seconds}} = \frac{2^{20} \text{ bits}}{86400 \text{ seconds}} = \frac{1048576}{86400} \text{ bits/second}$

4. Tebibits in base 2: $1 \text{ Tebibit} = 2^{40} \text{ bits}$

5. Putting it all together: $\frac{2^{20} \text{ bits}}{86400 \text{ seconds} \times 2^{40}} \text{ Tebibits/second} = \frac{2^{20}}{86400 \times 2^{40}} \text{ Tibit/s} = \frac{1}{86400 \times 2^{20}} \text{ Tibit/s} = \frac{1}{86400 \times 1048576} \text{ Tibit/s} = 1.35525271 \times 10^{-11} \text{ Tibit/s}$

Examples of Real-World Quantities in Megabits per Day

Here are some examples to provide context:

1. Household Internet Usage:

   • If a household uses about 100 GB of data in a month, that translates to approximately 25 Megabits per day (assuming 1 GB = 8,000 Megabits and an average month has 30 days).

2. Small Business Data Transfer:

   • A small business might back up 1 Terabyte (TB) of data over a week, which translates to approximately 1,142.857 Megabits per day (1 TB = 8,000,000 Megabits and 7 days in a week).

3. Streaming Services:

   • Streaming a standard definition video at about 3 Mbps continuously for 24 hours would result in 72 Megabits per day.

By breaking down the conversions into clear steps and contextualizing with real-world examples, you should have a good understanding of how to convert Megabits per day to Tebibits per second and can appreciate the relevance of these data transfer rates.