Bytes per second to Terabits per day conversion

How to convert bytes per second to terabits per day?

To convert data transfer rates from bytes per second (B/s) to terabits per day (Tb/day), you need to follow a series of unit conversions. Let's go through the steps for both base 10 (SI units) and base 2 (IEC units).

Base 10 (SI Units)

1. Convert bytes to bits: 1 byte (B) equals 8 bits (b).

2. Convert seconds to days: 1 day has 24 hours, each hour has 60 minutes, and each minute has 60 seconds. So, $1 \text{ day} = 24 \times 60 \times 60 \text{ seconds} = 86,400 \text{ seconds}$

3. Convert bits to terabits: 1 terabit (Tb) equals $10^{12}$ bits.

Putting it all together for 1 B/s:

$1 \text{ B/s} = 1 \times 8 \text{ b/s} = 8 \text{ b/s}$

Next, convert from seconds to days:

$8 \text{ b/s} \times 86,400 \text{ seconds/day} = 691,200 \text{ b/day}$

Finally, convert bits to terabits:

$691,200 \text{ b/day} = \frac{691,200}{10^{12}} \text{ Tb/day} = 0.0000006912 \text{ Tb/day} = 6.912 \times 10^{-7} \text{ Tb/day}$

Base 2 (IEC Units)

1. Convert bytes to bits: Same as before, 1 byte equals 8 bits.

2. Convert seconds to days: Same as before, $1 \text{ day} = 86,400 \text{ seconds}$

3. Convert bits to terabits: 1 terabit (TiB) in base 2 is $2^{40}$ bits.

Putting it all together for 1 B/s:

$1 \text{ B/s} = 1 \times 8 \text{ b/s} = 8 \text{ b/s}$

Next, convert from seconds to days:

$8 \text{ b/s} \times 86,400 \text{ seconds/day} = 691,200 \text{ b/day}$

Finally, convert bits to terabits (base 2):

$691,200 \text{ b/day} = \frac{691,200}{2^{40}} \text{ Tb/day} \approx \frac{691,200}{1,099,511,627,776} \approx 6.287 \times 10^{-7} \text{ Tb/day}$

Real World Examples

• 56 Kbps Dial-Up Internet (56,000 bits per second or 7,000 B/s):

  • Base 10: $7,000 \text{ B/s} = 4.838 \times 10^{-3} \text{ Tb/day}$
  • Base 2: $7,000 \text{ B/s} = 4.401 \times 10^{-3} \text{ Tb/day}$

• 1 Mbps Broadband Internet (1,000,000 bits per second or 125,000 B/s):

  • Base 10: $125,000 \text{ B/s} = 0.0864 \text{ Tb/day}$
  • Base 2: $125,000 \text{ B/s} = 0.0792 \text{ Tb/day}$

• 1 Gbps Fiber Internet (1,000,000,000 bits per second or 125,000,000 B/s):

  • Base 10: $125,000,000 \text{ B/s} = 86.4 \text{ Tb/day}$
  • Base 2: $125,000,000 \text{ B/s} = 79.2 \text{ Tb/day}$

These conversions highlight how data transfer rates can scale significantly across different orders of magnitude and units.