How this instrument works
Ancient Babylon used a positional counting system built on 60 rather than 10 — sexagesimal notation. A number splits into a high place (how many whole 60s it contains) and a low place (what's left over), the exact same idea as our own tens and ones columns, just built on a much larger base. The high place is found by dividing by 60 and dropping the remainder; the low place is whatever remains after that division.
This base didn't vanish with Babylon itself. Sixty has an unusually large number of divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30), which makes it easy to split into halves, thirds, quarters, fifths, and more without leaving an awkward fraction behind — likely why it stuck around for measuring time and angles specifically. Sixty minutes fill an hour, sixty seconds fill a minute, and 360 degrees (six lots of sixty) fill a full turn of a circle.
This site also has a companion page for the Mayan base-20 (vigesimal) system, which splits a number the same structural way but around a completely different base — comparing the two side by side makes it obvious that 'ones and tens' is just one arbitrary choice among many a civilization could have settled on.
- Enter a whole number from 0 to 3,599 into the Decimal number field.
- Read the High place: the count of full 60s contained in that number.
- Read the Low place: whatever remains once those 60s are removed.
- Multiply the high place by 60 and add the low place to confirm you land back on the original number.
Worked example — converting 125
The decimal number 125 divided by 60 gives 2 whole groups of 60 (that's 120), with 5 left over — so its Babylonian digits are high place 2 and low place 5. Checked in reverse: 2×60+5 = 125, exactly the number started with.
The largest number expressible with just these two places is 3,599 (59 full 60s plus a remainder of 59, since 60×60−1=3599) — one short of needing a third place, exactly the way 99 is the largest two-digit number before decimal counting needs a third column.
Questions
Why did the Babylonians count in base 60?
Sixty divides evenly by an unusually large set of numbers — 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 — which makes fractions like a third or a fifth land on a whole number of smaller units rather than an awkward remainder. That convenience is the leading explanation historians give for why it was chosen and why it stuck for so long.
Where does base 60 still show up today?
Timekeeping and angles: 60 seconds make a minute, 60 minutes make an hour, and 360 degrees (six sets of sixty) make a full circle. Every clock face and every compass bearing carries a trace of ancient Babylonian arithmetic.
What's the largest number this calculator can convert?
3,599 — the largest value expressible with exactly two base-60 places (59×60+59). A third digit would be needed to go any higher, the same way a third decimal digit is needed once a count passes 99.
How is this different from the Mayan Numeral page on this site?
Both split a decimal number into a high and low place using the identical division-and-remainder idea, but this page uses a base of 60 while the Mayan page uses a base of 20 — different civilizations, arrived at independently, choosing very different-sized groupings.
Did the Babylonians have a symbol for zero?
Only partially, and only later in their history — early Babylonian notation could be genuinely ambiguous about an empty place, and a dedicated placeholder symbol only appeared in later periods, unlike the fully developed zero digit used in modern positional systems.