Bytes per second to Kilobytes per hour conversion

How to convert bytes per second to kilobytes per hour?

To convert 1 byte per second (Bps) to kilobytes per hour, you need to understand the relationships between the units of time and data storage, and then perform the conversion accordingly.

1. Conversion Steps:

   • Time conversion: There are 60 seconds in a minute and 60 minutes in an hour. Therefore, there are 3600 seconds in an hour.

   • Data conversion in base 10 (SI units): In base 10, 1 Kilobyte (KB) is 1000 bytes (B).

   • Data conversion in base 2 (Binary units): In base 2, 1 Kibibyte (KiB) is 1024 bytes (B).

Base 10 (SI Units)

1. Time Conversion:

   $1 \text{ byte/second} \times 3600 \text{ seconds/hour} = 3600 \text{ bytes/hour}$

2. Data Conversion:

   $3600 \text{ bytes/hour} \div 1000 \text{ bytes/kilobyte} = 3.6 \text{ kilobytes/hour}$

Base 2 (Binary Units)

1. Time Conversion:

   $1 \text{ byte/second} \times 3600 \text{ seconds/hour} = 3600 \text{ bytes/hour}$

2. Data Conversion:

   $3600 \text{ bytes/hour} \div 1024 \text{ bytes/kibibyte} \approx 3.515625 \text{ kibibytes/hour}$

So, 1 byte per second is equivalent to:

• 3.6 kilobytes per hour (KB/hour) in base 10 (SI units).
• Approximately 3.515625 kibibytes per hour (KiB/hour) in base 2 (Binary units).

Real-World Examples for Other Quantities of Bytes per Second

1. 56 Kbps (Kilobits per second) Dial-Up Modem:

   • Conversion: 56 Kbps = 56,000 bits per second = 7,000 bytes per second (since 1 byte = 8 bits).

   • Base 10:

     • Per hour: $7,000 \text{ bytes/second} \times 3600 \text{ seconds/hour} = 25,200,000 \text{ bytes/hour}$
     • Kilobytes per hour: $25,200,000 \text{ bytes/hour} \div 1000 \approx 25,200 \text{ KB/hour}$

   • Base 2:

     • KiB per hour: $25,200,000 \text{ bytes/hour} \div 1024 \approx 24,609.375 \text{ KiB/hour}$

2. 1 Mbps (Megabit per second) Broadband Connection:

   • Conversion: 1 Mbps = 1,000,000 bits per second = 125,000 bytes per second.

   • Base 10:

     • Per hour: $125,000 \text{ bytes/second} \times 3600 \text{ seconds/hour} = 450,000,000 \text{ bytes/hour}$
     • Kilobytes per hour: $450,000,000 \text{ bytes/hour} \div 1000 = 450,000 \text{ KB/hour}$

   • Base 2:

     • KiB per hour: $450,000,000 \text{ bytes/hour} \div 1024 \approx 439,453.125 \text{ KiB/hour}$

3. 50 MBps (Megabytes per second) USB 3.0 connection:

   • Conversion: 50 MBps = 50,000,000 bytes per second.

   • Base 10:

     • Per hour: $50,000,000 \text{ bytes/second} \times 3600 \text{ seconds/hour} = 180,000,000,000 \text{ bytes/hour}$
     • Kilobytes per hour: $180,000,000,000 \text{ bytes/hour} \div 1000 = 180,000,000 \text{ KB/hour}$

   • Base 2:

     • KiB per hour: $180,000,000,000 \text{ bytes/hour} \div 1024 \approx 175,781,250 \text{ KiB/hour}$

These examples illustrate how different speeds translate to data transferred over time and highlight the differences in conversion between the base 10 and base 2 units.