Kilobits per day to Kilobytes per second conversion

How to convert kilobits per day to kilobytes per second?

To convert 1 Kilobit per day (kb/day) to Kilobytes per second (kB/s), we need to follow a step-by-step process. We need to recognize the difference between kilobits (Kb) and kilobytes (KB), and that there are two common bases used: base 10 (decimal) and base 2 (binary).

Basic Steps for Conversion

1. Convert Kilobits to Bits: Since 1 kilobit (Kbit) is 1000 bits in base 10 and 1024 bits in base 2.

2. Convert Bits to Seconds: There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Total seconds in a day = 24 * 60 * 60 = 86400 seconds

3. Convert Bits per Second to Kilobytes per Second: Since 1 kilobyte (KB) is 1000 bytes in base 10 and 1024 bytes in base 2, each byte is 8 bits.

Base 10 Conversion (Decimal)

1. Convert Kilobits to Bits: 1 Kbit/day = 1000 bits/day

2. Convert Bits per Day to Bits per Second: $\frac{1000 \text{ bits}}{86400 \text{ seconds}} \approx 0.01157 \text{ bits/second}$

3. Convert Bits per Second to Kilobytes per Second: $0.01157 \text{ bits/second} \div 8 \approx 0.001446 \text{ bytes/second}$ $0.001446 \text{ bytes/second} \div 1000 \approx 0.000001446 \text{ kB/s}$

Base 2 Conversion (Binary)

1. Convert Kilobits to Bits: 1 Kbit/day = 1024 bits/day

2. Convert Bits per Day to Bits per Second: $\frac{1024 \text{ bits}}{86400 \text{ seconds}} \approx 0.01185 \text{ bits/second}$

3. Convert Bits per Second to Kilobytes per Second: $0.01185 \text{ bits/second} \div 8 \approx 0.001481 \text{ bytes/second}$ $0.001481 \text{ bytes/second} \div 1024 \approx 0.000001447 \text{ kB/s}$

Real World Examples for Other Quantities

Let's consider some larger quantities of Kilobits per day for a practical understanding:

Example: 1 Megabit per Day

1 Megabit (Mbit) is 1000 Kilobits (Kbit) in base 10.

• Base 10:

  • $1 \text{ Mbit/day} = 1000 \text{ Kbit/day}$
  • $\frac{1000 \times 1000 \text{ bits}}{86400 \text{ seconds}} \approx 11.57 \text{ bits/second}$
  • $11.57 \text{ bits/second} \div 8 \approx 1.446 \text{ bytes/second}$
  • $1.446 \text{ bytes/second} \div 1000 \approx 0.001446 \text{ kB/s}$

• Base 2:

  • $1 \text{ Mbit/day} = 1024 \text{ Kbit/day}$
  • $\frac{1024 \times 1024 \text{ bits}}{86400 \text{ seconds}} \approx 12.02 \text{ bits/second}$
  • $12.02 \text{ bits/second} \div 8 \approx 1.502 \text{ bytes/second}$
  • $1.502 \text{ bytes/second} \div 1024 \approx 0.001466 \text{ kB/s}$

Example: 1 Gigabit per Day

1 Gigabit (Gbit) is 1000 Megabits (Mbit) in base 10.

• Base 10:

  • $1 \text{ Gbit/day} = 1000 \text{ Mbit/day} = 1000000 \text{ Kbit/day}$
  • $\frac{1000000 \times 1000 \text{ bits}}{86400 \text{ seconds}} \approx 11574.1 \text{ bits/second}$
  • $11574.1 \text{ bits/second} \div 8 \approx 1446.76 \text{ bytes/second}$
  • $1446.76 \text{ bytes/second} \div 1000 \approx 1.447 \text{ kB/s}$

• Base 2:

  • $1 \text{ Gbit/day} = 1024 \text{ Mbit/day} = 1048576 \text{ Kbit/day}$
  • $\frac{1048576 \times 1024 \text{ bits}}{86400 \text{ seconds}} \approx 12022 \text{ bits/second}$
  • $12022 \text{ bits/second} \div 8 \approx 1502.72 \text{ bytes/second}$
  • $1502.72 \text{ bytes/second} \div 1024 \approx 1.467 \text{ kB/s}$

By following the respective conversion steps based on base 10 and base 2, it becomes easier to understand how these values translate into real-world data transfer rates.