base26

Base26 refers to a numeral system that uses 26 distinct symbols, typically the letters A through Z, as its digits. In general, a base-b system represents integers as sums of powers of b with digits ranging from 0 to b−1. When the symbols are letters, base-26 is often used for labeling, encoding, or compact alphabetic representations rather than for arithmetic in the usual sense.

There are two common conventions. Zero-based base-26 uses the 26 digits 0 through 25, which can be mapped to letters in various ways and is primarily a mathematical convenience rather than a labeling scheme. Bijective base-26, commonly seen in spreadsheet column labels, uses digits A through Z corresponding to values 1 through 26, with no zero digit. In this system, 1 maps to A, 26 to Z, 27 to AA, 28 to AB, and so on. This bijective form is non‑standard for pure arithmetic but is convenient for human-facing labels.

Conversion to bijective base-26 involves repeatedly subtracting 1, dividing by 26, and mapping remainders to letters. For example, 1 → A, 26 → Z, 27 → AA, 28 → AB. This convention underpins how spreadsheet programs label columns.

Applications include labeling schemes, such as spreadsheet columns, inventory codes, and simple alphabetic encodings. Base-26 is not a general-purpose numeric base for computation in most programming languages, and the existence of multiple conventions can lead to ambiguity without explicit specification.