Babylonian Base-60 Converter
Enter a whole number to convert it to base-60 (sexagesimal).
Result
How it is calculated
The tool repeatedly divides the whole number by 60. Each remainder (0 to 59) is one sexagesimal digit, found with digit = n mod 60 followed by n = ⌊n ÷ 60⌋ until n reaches 0. The remainders are then read in reverse order, so the last one found is the leftmost, most significant digit. Digits are written in ordinary decimal and separated by commas, and the tool also reports how many base-60 digits there are. The place values are 600 = 1, 601 = 60, 602 = 3,600 and so on. Input is rounded to the nearest whole number (59.6 becomes 60, shown as 1,0), negative numbers give no result, and 0 is shown as a single 0.
Worked example
Convert 7384. 7,384 ÷ 60 = 123 remainder 4, so the last digit is 4. 123 ÷ 60 = 2 remainder 3, so the middle digit is 3. 2 ÷ 60 = 0 remainder 2, so the first digit is 2. Reading the remainders backwards gives 2,3,4, which has 3 digits. Check: 2 × 3,600 + 3 × 60 + 4 = 7,200 + 180 + 4 = 7,384.
Common mistakes
- Reading the commas as decimal commas or thousands separators. In 2,3,4 each comma only separates the base-60 digits; it is not 2.34 or 234.
- Reading each digit as a separate decimal digit. A base-60 digit can be as high as 59, so "1,59" means 1 × 60 + 59 = 119, not 159.
- Entering a fraction and expecting a sexagesimal fraction. The tool handles whole numbers only and rounds anything else, so 59.6 becomes 60.
- Expecting empty places to vanish. A zero in a middle place stays in the output (3600 is 1,0,0); the Babylonians themselves marked it only with a gap or later a placeholder sign, so original tablets can be ambiguous.
- Confusing it with hours, minutes and seconds. 7384 seconds is 2:03:04 as a clock reading, which resembles 2,3,4 here, but the tool is a pure place-value conversion.
About this calculator
The Babylonians, who dominated Mesopotamian mathematics from roughly 2000 BCE, wrote numbers in a sexagesimal (base-60) positional system rather than base-10. Each position represents a power of 60 instead of a power of 10, so a value like 83 becomes "1,23" — one group of 60 plus 23 units — using cuneiform wedge-and-hook symbols built from just two glyphs repeated up to 59 times. Base 60 survives today in how we split hours into minutes and seconds, and degrees into arcminutes and arcseconds, precisely because the Babylonians chose it for its rich divisibility (60 has twelve divisors, versus four for 10).
This calculator takes a decimal whole number and breaks it into its base-60 place values, showing each sexagesimal digit the way a Babylonian scribe would have arranged them on a clay tablet. Historians of mathematics, educators teaching numeral systems, and students studying ancient Mesopotamia use it to see the mechanics of a place-value system that predates decimal notation by millennia, and to check hand conversions when working through cuneiform tablet transcriptions.
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