Terabits per day to Gigabytes per second conversion

How to convert terabits per day to gigabytes per second?

To convert from Terabits per day (Tb/day) to Gigabytes per second (GB/s), you'll need to follow several steps involving unit conversions. It's important to note the distinction between base 10 (decimal) and base 2 (binary) conversions, as data measurements can differ depending on which base is used.

Base 10 (Decimal) Conversion

1. Understand the units:

   • 1 Terabit (Tb) = 10^12 bits
   • 1 Gigabyte (GB) = 10^9 bytes
   • 1 byte = 8 bits

2. Convert Terabits to bits: $1 \text{ Tb} = 10^{12} \text{ bits}$

3. Convert bits to bytes: $1 \text{ Tb} = \frac{10^{12}}{8} \text{ bytes}$

4. Convert bytes to Gigabytes: $1 \text{ Tb} = \frac{10^{12}}{8 \times 10^9} \text{ GB} = 125 \text{ GB}$

5. Convert per day to per second:

   • There are 86400 seconds in a day.

   $\text{Data rate in GB/s} = \frac{125 \text{ GB}}{86400 \text{ s}} \approx 0.001446 \text{ GB/s}$

Base 2 (Binary) Conversion

1. Understand the units:

   • 1 Terabit (Tb) = 2^40 bits
   • 1 Gigabyte (GiB, using binary base) = 2^30 bytes
   • 1 byte = 8 bits

2. Convert Terabits to bits: $1 \text{ Tb} = 2^{40} \text{ bits}$

3. Convert bits to bytes: $1 \text{ Tb} = \frac{2^{40}}{8} \text{ bytes} = 2^{37} \text{ bytes}$

4. Convert bytes to Gibibytes: $1 \text{ Tb} = \frac{2^{37}}{2^{30}} \text{ GiB} = 2^7 \text{ GiB} = 128 \text{ GiB}$

5. Convert per day to per second:

   • There are 86400 seconds in a day.

   $\text{Data rate in GiB/s} = \frac{128 \text{ GiB}}{86400 \text{ s}} \approx 0.001481 \text{ GiB/s}$

Real-World Examples Using Other Quantities:

1. 5 Terabits per day:

   • Base 10 Conversion: $\text{Data rate in GB/s} = 5 \times 0.001446 \text{ GB/s} = 0.00723 \text{ GB/s}$

   • Base 2 Conversion: $\text{Data rate in GiB/s} = 5 \times 0.001481 \text{ GiB/s} = 0.007405 \text{ GiB/s}$

2. 10 Terabits per day:

   • Base 10 Conversion: $\text{Data rate in GB/s} = 10 \times 0.001446 \text{ GB/s} = 0.01446 \text{ GB/s}$

   • Base 2 Conversion: $\text{Data rate in GiB/s} = 10 \times 0.001481 \text{ GiB/s} = 0.01481 \text{ GiB/s}$

3. 20 Terabits per day:

   • Base 10 Conversion: $\text{Data rate in GB/s} = 20 \times 0.001446 \text{ GB/s} = 0.02892 \text{ GB/s}$

   • Base 2 Conversion: $\text{Data rate in GiB/s} = 20 \times 0.001481 \text{ GiB/s} = 0.02962 \text{ GiB/s}$

These conversions help you understand the data rates in gigabytes per second, providing a clear picture of how much data would be transferred over different timescales using both decimal and binary measuring conventions.