Kilobits per hour to Gigabits per month conversion

How to convert kilobits per hour to gigabits per month?

Sure, let's go through the conversion step-by-step for both base 10 (decimal) and base 2 (binary) units.

Base 10 (Decimal) Conversion

1. Starting Conversion Factors:

   • 1 kilobit (kb) = 1,000 bits
   • 1 gigabit (Gb) = 1,000,000,000 bits
   • 1 hour = 60 minutes
   • 1 minute = 60 seconds
   • 1 day = 24 hours
   • 1 month ≈ 30 days (for approximation)

2. Steps:

   • Kilobits per hour to bits per hour: $1 \text{ kb/hr} = 1,000 \text{ bits/hr}$
   • Bits per hour to bits per day: $1,000 \text{ bits/hr} \times 24 \text{ hr/day} = 24,000 \text{ bits/day}$
   • Bits per day to bits per month: $24,000 \text{ bits/day} \times 30 \text{ days/month} = 720,000 \text{ bits/month}$
   • Bits per month to gigabits per month: $\frac{720,000 \text{ bits/month}}{1,000,000,000 \text{ bits/Gb}} = 0.00072 \text{ Gb/month}$

Base 2 (Binary) Conversion

1. Starting Conversion Factors:

   • 1 kibibit (Kib) = 1,024 bits
   • 1 gibibit (Gib) = 1,024^3 = 1,073,741,824 bits
   • Other time-related conversions (hours, days, months) remain the same as in base 10.

2. Steps:

   • Kilobits per hour to bits per hour (using kibibits): $1 \text{ Kib/hr} = 1,024 \text{ bits/hr}$
   • Bits per hour to bits per day: $1,024 \text{ bits/hr} \times 24 \text{ hr/day} = 24,576 \text{ bits/day}$
   • Bits per day to bits per month: $24,576 \text{ bits/day} \times 30 \text{ days/month} = 737,280 \text{ bits/month}$
   • Bits per month to gibibits per month: $\frac{737,280 \text{ bits/month}}{1,073,741,824 \text{ bits/Gib}} \approx 0.000686 \text{ Gib/month}$

Real World Examples

• Internet Speed:

  • If a connection speed is 128 kb/hr: $\text{Base 10: } \frac{128 \times 720,000}{1,000,000,000} = 0.09216 \text{ Gb/month}$ $\text{Base 2: } \frac{128 \times 737,280}{1,073,741,824} \approx 0.087744 \text{ Gib/month}$

• Usage Monitoring:

  • A smart thermostat transmitting data at 5 kb/hr: $\text{Base 10: } \frac{5 \times 720,000}{1,000,000,000} = 0.0036 \text{ Gb/month}$ $\text{Base 2: } \frac{5 \times 737,280}{1,073,741,824} \approx 0.00343 \text{ Gib/month}$

• File Uploads:

  • A surveillance camera uploading footage at 50 kb/hr: $\text{Base 10: } \frac{50 \times 720,000}{1,000,000,000} = 0.036 \text{ Gb/month}$ $\text{Base 2: } \frac{50 \times 737,280}{1,073,741,824} \approx 0.0343 \text{ Gib/month}$

Summary

• 1 kilobit per hour is equivalent to 0.00072 gigabits per month in base 10.
• 1 kilobit per hour is approximately 0.000686 gibibits per month in base 2.