Babylonian Numbers Converter

The Babylonian number system operated on a base-60 (sexagesimal) positional framework, documented on clay tablets from roughly 2000 BCE onward. Each positional digit is expressed using only two mark types: a vertical wedge (𒐕) representing 1 and a corner wedge or Winkelhaken (𒌋) representing 10. Digits range from 0 to 59. A value like 75 in decimal becomes 1×60 + 15, written as one unit-wedge followed by one corner-wedge and five unit-wedges in the next lower place. Misreading positional place values or the absence of a zero marker led to genuine ambiguity on historical tablets. This tool computes exact sexagesimal decomposition and renders authentic cuneiform glyphs so the conversion is verifiable, not decorative.

The system lacked a true zero until the Seleucid era (c. 300 BCE), when a placeholder symbol appeared. This converter supports both conventions. Note: the tool approximates display for values up to 12,959,999 (60⁴ − 1). Fractional sexagesimal (used in Babylonian astronomy) is not handled here. For scholarly transliteration, always cross-reference with the original tablet context, as spacing between digit groups was the only delimiter available to ancient scribes.

Babylonian notation is positional base-60. A number N with k sexagesimal digits d_k−1, d_k−2, …, d₀ expands as:

where each digit d_i satisfies 0 ≤ d_i ≤ 59.

To convert decimal N to sexagesimal, extract digits by repeated Euclidean division:

Each digit d_i is then decomposed into cuneiform marks: t = ⌊d_i ÷ 10⌋ corner-wedges and u = d_i mod 10 vertical wedges.

Where N = input decimal integer, d_i = sexagesimal digit at position i, k = total number of sexagesimal places, t = count of ten-wedges (𒌋), u = count of unit-wedges (𒐕).