Babylonian Sexagesimal (Base 60) Converter — Decimal ⇄ Cuneiform
Convert a whole number between decimal and Babylonian base-60 (sexagesimal). See every place as a 0–59 value in comma notation, the ×3600 / ×60 / ×1 positional expansion, and a cuneiform rendering built from tens 𒌋 and units 𒁹 signs. Two-way and live in your browser.
How to Use
- Pick whether you are typing a decimal number, base-60 comma notation, or cuneiform.
- Enter your value — every other representation updates instantly.
- Read each place as a digit 0–59; the positional expansion shows the ×3600 / ×60 / ×1 working.
- Click any value (or its Copy button) to copy it, including the cuneiform glyphs.
Counting in sixties
The Babylonians built one of the oldest positional number systems in the world, and they did it in base 60 rather than base 10. Just like our decimal system, each column is worth a power of the base — but instead of ones, tens and hundreds the columns are worth 1, 60, 3600 (60²), 216000 (60³) and so on. Each column holds a single digit from 0 to 59. To convert a decimal number you repeatedly divide by 60, writing down each remainder; reading those remainders from the last division back to the first gives the base-60 digits. Modern scholars separate the digits with commas, so 3661 = 1,1,1 means 1×3600 + 1×60 + 1×1.
Wedges within each place
Within a single 0–59 digit the Babylonians used a clever sub-system of just two cuneiform signs pressed into clay with a stylus: a vertical units wedge 𒁹 worth 1, and a corner tens wedge 𒌋 worth 10. A digit is written as the right number of tens followed by the right number of units, so 23 is two tens and three units (𒌋𒌋 𒁹𒁹𒁹) and 5 is simply five units. This makes the whole system a hybrid: base 60 between the columns, but a tally of tens and ones inside each column. The table above breaks every place down into its tens-and-units count and its ×weight contribution.
Why it still runs your clock
Sixty is unusually convenient: it divides evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, which makes fractions tidy. That practicality is why base 60 outlived Babylon and still governs how we measure time (60 seconds, 60 minutes) and angles (360° = 6×60, each degree split into 60 arcminutes and 60 arcseconds). When this tool turns 3661 into 1,1,1 it is doing exactly the same arithmetic that turns 3661 seconds into 1 hour, 1 minute and 1 second.
Quick reference
About the Babylonian Sexagesimal (Base 60) Converter — Decimal ⇄ Cuneiform
Meet the Babylonian Sexagesimal (Base 60) Converter — Decimal ⇄ Cuneiform: a free, no-fuss tool for everyday tasks with nothing to install and no sign-up. Convert a whole number between decimal and Babylonian base-60 (sexagesimal). See every place as a 0–59 value in comma notation, the ×3600 / ×60 / ×1 positional expansion, and a cuneiform rendering built from tens 𒌋 and units 𒁹 signs. Two-way and live in your browser.
How it works
Type a value, then pick what you want to change it into. The answer appears straight away. It all happens on your own device, so it is fast and nothing you type is sent away. Just check that you picked the right “from” and “to” so you get the answer you wanted.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
What is the Babylonian sexagesimal system?
It is a positional number system in base 60, used in ancient Mesopotamia roughly 4,000 years ago. Like our decimal system each column is worth a power of the base — but the base is 60, so the columns are worth 1, 60, 3600, 216000 and so on. Each place holds a digit from 0 to 59, which the Babylonians themselves wrote with two cuneiform signs: a units wedge 𒁹 and a tens wedge 𒌋.
How do I read the comma notation?
Modern scholars write a sexagesimal number as its place values separated by commas, most-significant first. So 1,1,1 means 1×3600 + 1×60 + 1×1 = 3661, and 2,5 means 2×60 + 5 = 125. Each group between commas is a single base-60 digit and must be in the range 0–59.
Why is there a note about “no true zero”?
Early Babylonian maths had no symbol for zero, so an empty column was just left blank — context told you whether “1 1” meant 61 or 3601. A placeholder sign was only introduced later, and it was never used at the end of a number. Our converter shows a real 0 for empty columns so the value is unambiguous, but historically that zero did not exist.
Where is base 60 still used today?
Everywhere you measure time and angles: 60 seconds in a minute, 60 minutes in an hour, and 360 = 6×60 degrees in a circle (each split into 60 arcminutes and 60 arcseconds). These conventions are a direct inheritance from Babylonian astronomy.
Is anything uploaded?
No. The whole conversion runs in your browser with JavaScript — nothing is sent to a server.
How do I use the Babylonian Sexagesimal (Base 60) Converter — Decimal ⇄ Cuneiform?
Just type or paste your value. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
History & maths teaching
Show students how a positional system works in an unfamiliar base, and where our clocks and protractors come from.
Reading cuneiform tablets
Turn a transliterated 0–59 place sequence into a decimal value, or render a decimal number back into wedge signs.
Time & angle intuition
See why 3661 seconds is 1:01:01 — the same 1,1,1 that base 60 produces for hours, minutes and seconds.
Puzzles & worldbuilding
Generate authentic-looking sexagesimal numerals for games, fiction or escape-room clues.
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