Mebibytes per day to Gigabytes per second conversion

How to convert mebibytes per day to gigabytes per second?

To convert 1 Mebibyte per day (MiB/day) to Gigabytes per second (GB/s), you need to perform a series of conversions involving both time and data units. Here, I'll show you the conversions for both base 2 (binary) and base 10 (decimal) units.

Base 2 Conversion (Binary)

Mebibytes and Gibibytes are based on powers of 2.

1 Mebibyte (MiB) = 2^20 bytes = 1,048,576 bytes 1 Gibibyte (GiB) = 2^30 bytes = 1,073,741,824 bytes

We need to first convert days to seconds. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute:

1 day = 24 hours × 60 minutes × 60 seconds = 86,400 seconds

Next, we convert 1 Mebibyte per day to bytes per second:

$\text{Bytes per second} = \frac{1,048,576 \text{ bytes}}{86,400 \text{ seconds}} \approx 12.13 \text{ bytes/second}$

Then, convert bytes per second to Gibibytes per second:

$\text{GiB/second} = \frac{12.13 \text{ bytes/second}}{1,073,741,824 \text{ bytes/GiB}} \approx 1.13 \times 10^{-8} \text{ GiB/second}$

Since 1 GiB = 2^30 bytes, we can also use this when converting from bytes per second to GiB per second, thus, $12.13 \text{ bytes/second} / 1,073,741,824 \approx 1.13 \times 10^{-8} \text{ GiB/second}$

Base 10 Conversion (Decimal)

Megabytes and Gigabytes in a base 10 system are based on powers of 10.

1 Megabyte (MB) = 10^6 bytes = 1,000,000 bytes 1 Gigabyte (GB) = 10^9 bytes = 1,000,000,000 bytes

Again, convert days to seconds:

1 day = 86,400 seconds

Next, convert 1 Megabyte per day to bytes per second:

$\text{Bytes per second} = \frac{1,000,000 \text{ bytes}}{86,400 \text{ seconds}} \approx 11.57 \text{ bytes/second}$

Then, convert bytes per second to Gigabytes per second:

$\text{GB/second} = \frac{11.57 \text{ bytes/second}}{1,000,000,000 \text{ bytes/GB}} = 1.157 \times 10^{-8} \text{ GB/second}$

Summary

• In Base 2 (Binary): $1 \text{ MiB/day} \approx 1.13 \times 10^{-8} \text{ GiB/second}$
• In Base 10 (Decimal): $1 \text{ MB/day} \approx 1.157 \times 10^{-8} \text{ GB/second}$

Real World Examples

Here are conversions of some other quantities of Mebibytes per day to give you context:

1. 10 MiB/day:

   • Binary: $10 \times 1.13 \times 10^{-8} \approx 1.13 \times 10^{-7}$ GiB/second
   • Decimal: $10 \times 1.157 \times 10^{-8} \approx 1.157 \times 10^{-7}$ GB/second

2. 100 MiB/day:

   • Binary: $100 \times 1.13 \times 10^{-8} \approx 1.13 \times 10^{-6}$ GiB/second
   • Decimal: $100 \times 1.157 \times 10^{-8} \approx 1.157 \times 10^{-6}$ GB/second

3. 1 GiB/day (since 1 GiB = 1024 MiB):

   • Binary: $1024 \times 1.13 \times 10^{-8} \approx 1.157 \times 10^{-5}$ GiB/second
   • Decimal (using MB): $1073.74 \times 1.157 \times 10^{-8} \approx 1.157 \times 10^{-5}$ GB/second

Conclusion

By understanding these conversions, you have a tool for relating data transfer rates across different units and time intervals, crucial for various practical applications in data management, networking, and IT.