bits per second to Terabits per day conversion

How to convert bits per second to terabits per day?

To convert 1 bit per second (bps) to Terabits per day, you need to consider the number of seconds in a day and the number of bits in a Terabit.

There are 86,400 seconds in a day (since 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds).

Next, there are two different systems for calculating larger units: base 10 (SI units) and base 2 (binary units):

Base 10 (SI Units)

1 Terabit (Tb) = 10^12 bits

To find out how many Terabits per day:

$1 \text{ bps} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$

Now, convert bits/day to Terabits/day:

$\frac{86,400 \text{ bits}}{10^{12}} = 8.64 \times 10^{-8} \text{ Terabits/day}$

Base 2 (Binary Units)

1 Tebibit (Tib) = 2^40 bits

Using the same formula for seconds in a day:

$1 \text{ bps} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$

Now, convert bits/day to Tebibits/day:

$\frac{86,400 \text{ bits}}{2^{40}} \approx 7.844 \times 10^{-11} \text{ Tebibits/day}$

Summary

• Base 10: $1 \text{ bps} = 8.64 \times 10^{-8} \text{ Terabits/day}$
• Base 2: $1 \text{ bps} = 7.844 \times 10^{-11} \text{ Tebibits/day}$

Real-world Examples for Other Quantities of Bits per Second:

1. Dial-up Internet Speed: A typical dial-up connection offers speeds of about 56 Kbps (kilobits per second).

   • In Base 10: $56 \text{ Kbps} = 56,000 \text{ bps}$ $56,000 \times 86,400 = 4,838,400,000 \text{ bits/day} = 4.8384 \times 10^{-3} \text{ Terabits/day}$

   • In Base 2: $56 \text{ Kbps} = 54,687.5 \text{ Kibps}$ $54,687.5 \times 86,400 = 4,724,563,200 \text{ Kib/day} = 4.724 \times 10^{-6} \text{ Tebibits/day}$

2. Standard Home Broadband: Typical broadband speeds can range from 100 Mbps to 1 Gbps (Gigabit per second).

   • For 100 Mbps (Base 10): $100,000,000 \text{ bps}$ $100,000,000 \times 86,400 = 8.64 \times 10^{12} \text{ bits/day} = 8.64 \text{ Terabits/day}$

   • In Base 2: $100,000 \times 1024 = 102,400,000 \text{ Kibps}$ $102,400,000 \times 86,400 \approx 8.813 \times 10^{12} \text{ Kib/day} = 8.131 \text{ Tib/day}$

3. Corporate Network: Large corporations may deal with speeds of 10 Gbps or higher.

   • For 10 Gbps (Base 10): $10,000,000,000 \text{ bps}$ $10,000,000,000 \times 86,400 = 8.64 \times 10^{14} \text{ bits/day} = 864 \text{ Terabits/day}$

   • In Base 2: $10,000,000 \times 1024 = 10,485,760,000 \text{ Kibps}$ $10,485,760,000 \times 86,400 \approx 9.05 \times 10^{14} \text{ Kib/day} = 9.847 \times \times 10^{11}\text{ Tib/day}$

These examples highlight the significant difference in data throughput when transferring bits per second into daily data volume using both base 10 and base 2 measurements.