File Size Calculation and Data Storage Units

Data Storage Units

The distinction between binary (KiB, MiB, GiB) and decimal (KB, MB, GB) units causes confusion in file sizes, storage capacity, and bandwidth calculations.

Binary vs Decimal Units

Binary: 1 KiB = 1,024 bytes (2^10). 1 MiB = 1,048,576 bytes (2^20). 1 GiB = 1,073,741,824 bytes (2^30). Decimal: 1 KB = 1,000 bytes (10^3). 1 MB = 1,000,000 bytes (10^6). 1 GB = 1,000,000,000 bytes (10^9). The difference grows with scale: 1 TB (decimal) is 931 GiB (binary). This is why your "1 TB" hard drive shows ~931 GB in your operating system.

Who Uses Which

Hard drive and SSD manufacturers use decimal units (makes their drives appear larger). Operating systems historically used binary units but labeled them with decimal prefixes. Network speeds use decimal: 100 Mbps = 100,000,000 bits per second. RAM uses binary: 8 GB of RAM = 8 GiB = 8,589,934,592 bytes.

Bandwidth Calculations

Network speeds are measured in bits, storage in bytes. 1 byte = 8 bits. A 100 Mbps connection transfers a maximum of 12.5 MB/s (100/8). In practice, overhead (protocol headers, retransmissions) reduces this by 5-10%. A 1 GB file takes approximately 85 seconds on a 100 Mbps connection: 1,000 MB / 11.75 MB/s effective.

Image and Video File Size Estimation

Uncompressed image size: width × height × bytes per pixel (3 for RGB, 4 for RGBA). A 4000×3000 RGB image = 36 MB uncompressed. JPEG compression typically achieves 10:1, so ~3.6 MB. Uncompressed video: width × height × 3 × fps × seconds. 1080p at 30fps for 60 seconds = 5.6 GB uncompressed. H.264 compression achieves roughly 50:1-200:1 depending on content.

Practical Conversions

Quick mental math: divide bytes by 1 million for MB (close enough for estimation). 15,728,640 bytes ≈ 15 MB. For precise conversion, divide by 1,048,576 for MiB: 15,728,640 / 1,048,576 = 15.0 MiB. For bandwidth: divide Mbps by 8 for MB/s. 50 Mbps ≈ 6 MB/s download speed.