The Mathematics of Decimal (SI) vs. Binary (IEC) Data Storage
For decades, confusion has surrounded storage capacity ratings. The root of the dilemma lies in the conflict between human decimal arithmetic (Base 10) and computer binary architecture (Base 2):
• Decimal SI Standards (Base 10): Storage drive manufacturers (Western Digital, Seagate, Samsung) use SI metric prefixes: $1\text{ Kilobyte (KB)} = 10^3 = 1,000\text{ bytes}$, and $1\text{ Gigabyte (GB)} = 10^9 = 1,000,000,000\text{ bytes}$.
• Binary IEC Standards (Base 2): Computers operate on binary electrical transistors where memory addresses scale by powers of two: $1\text{ Kibibyte (KiB)} = 2^{10} = 1,024\text{ bytes}$, and $1\text{ Gibibyte (GiB)} = 2^{30} = 1,073,741,824\text{ bytes}$.
Data Storage Hierarchy Reference Table
| Prefix Name | Standard Symbol | Base (Formula) | Exact Number of Bytes | Relative Size Ratio |
|---|---|---|---|---|
| Kilobyte (SI) | KB | 10³ | 1,000 | Baseline metric |
| Kibibyte (IEC) | KiB | 2¹⁰ | 1,024 | +2.4% larger than KB |
| Megabyte (SI) | MB | 10⁶ | 1,000,000 | Baseline metric |
| Mebibyte (IEC) | MiB | 2²⁰ | 1,048,576 | +4.86% larger than MB |
| Gigabyte (SI) | GB | 10⁹ | 1,000,000,000 | Baseline metric |
| Gibibyte (IEC) | GiB | 2³⁰ | 1,073,741,824 | +7.37% larger than GB |
| Terabyte (SI) | TB | 10¹² | 1,000,000,000,000 | Baseline metric |
| Tebibyte (IEC) | TiB | 2⁴⁰ | 1,099,511,627,776 | +9.95% larger than TB |
Why the Discrepancy Grows Exponentially With Larger Drives
At the Kilobyte level, the difference between $10^3$ (1,000) and $2^{10}$ (1,024) is a minor $2.4\%$. However, with each progressive power step, the compounded difference widens. By the time you reach Terabytes ($10^{12}$ vs $2^{40}$), the difference is nearly $10\%$. This is why buying a 16 TB enterprise NAS drive only displays approximately 14.55 TiB of space when formatted in Windows.
Frequently Asked Questions (FAQ)
Does Apple macOS calculate drive sizes the same way as Windows?
No. Starting with Mac OS X Snow Leopard (10.6), Apple modified macOS to calculate file and disk sizes in decimal Base 10 (1 GB = 1,000,000,000 bytes). Consequently, a 1 TB external SSD displays as exactly 1.0 TB on a Mac, but displays as 931 GB on Windows.
What is the difference between Megabits (Mb) and Megabytes (MB)?
Internet speeds are quoted in bits (e.g. 100 Mbps broadband), while files are measured in bytes (e.g. 500 MB video). Since 1 byte = 8 bits, divide your broadband Mbps speed by 8 to determine your real-world maximum download speed in MB/s.
What is File System Overhead (NTFS / EXT4)?
When you format a disk, a small percentage of raw space is allocated to partition tables, the Master File Table (MFT), journaling logs, and bad-sector reserves. This accounts for an additional 1% to 2% reduction in usable storage space.