Mebibytes per second to Terabytes per hour conversion

How to convert mebibytes per second to terabytes per hour?

To convert 1 Mebibyte per second (MiB/s) to Terabytes per hour, we need to understand both base 2 and base 10 definitions, as they provide different results.

Base 2 Calculation

1 Mebibyte (MiB) = 2^20 bytes = 1,048,576 bytes. 1 Terabyte (TB) = 2^40 bytes = 1,099,511,627,776 bytes.

First, convert 1 MiB to bytes: 1 MiB/s * 1,048,576 bytes/MiB = 1,048,576 bytes/second.

Next, convert seconds to hours (3600 seconds in an hour): 1,048,576 bytes/second * 3600 seconds/hour = 3,775,329,280 bytes/hour.

Finally, convert bytes/hour to Terabytes: 3,775,329,280 bytes/hour ÷ 1,099,511,627,776 bytes/TB ≈ 0.003435 Terabytes/hour.

Base 10 Calculation

1 Megabyte (MB, base 10) = 10^6 bytes = 1,000,000 bytes. 1 Terabyte (TB, base 10) = 10^12 bytes = 1,000,000,000,000 bytes.

First, convert 1 MiB to MB (using base 2 to base 10 conversion for this step): 1 MiB = 1,048,576 bytes. 1 MB = 1,000,000 bytes. So, 1 MiB = 1.048576 MB.

Then convert 1 MiB to bytes: 1 MiB/s * 1,048,576 bytes/MiB = 1,048,576 bytes/second.

Convert seconds to hours (3600 seconds in an hour): 1,048,576 bytes/second * 3600 seconds/hour = 3,775,329,280 bytes/hour.

Finally, convert bytes/hour to Terabytes: 3,775,329,280 bytes/hour ÷ 1,000,000,000,000 bytes/TB ≈ 0.003775 Terabytes/hour.

Summary

• Base 2: 1 MiB/s ≈ 0.003435 TB/hour.
• Base 10: 1 MiB/s ≈ 0.003775 TB/hour.

Real World Examples

1. Downloading a High-Resolution Movie:

   • A 4K movie might have a size of about 100 GB (Gigabytes).
   • If you have a download speed of 3 MiB/s, it would take approximately: $\frac{100 \text{ GB} \times 1024 \text{ MB/GB}}{3 \text{ MiB/s}} \approx 34133.33 \text{ seconds} \approx 9.48 \text{ hours}$
   • Note: Conversion is simplified for example purposes.

2. Streaming Full HD Video:

   • Full HD streaming can require about 5 MiB/s.
   • For a 2-hour movie, you'd need: $5 \text{ MiB/s} \times 2 \text{ hours} \times 3600 \text{ seconds/hour} \approx 36,000 \text{ MiB} \approx 35.16 \text{ GiB}$

3. Backing Up Data to Cloud:

   • Backing up 500 GiB with an upload speed of 10 MiB/s: $\frac{500 \text{ GiB} \times 1024 \text{ MiB/GiB}}{10 \text{ MiB/s}} \approx 51,200 \text{ seconds} \approx 14.22 \text{ hours}$

By understanding these conversion processes and examples, you can get a grasp on how data transfer rates impact real-world scenarios.