How Base64 Encoding Works: Radix-64 Bit Splitting, 33% Payload Expansion, and Web Performance

2. The 24-Bit to 32-Bit Transformation Mathematics

Base64 groups 3 consecutive 8-bit bytes (a total of 24 bits) and splits them into 4 separate 6-bit groups. Because $2^6 = 64$, each 6-bit value indexes cleanly into a standard 64-character alphabet (A-Z, a-z, 0-9, +, /). Because 3 bytes become 4 characters, the data payload inevitably expands by exactly:

Expansion Ratio = 4 / 3 = 1.3333... (+33.3% overhead)