How this instrument works
Several Mesoamerican civilizations, the Maya among them, built their number system around a base of 20 rather than 10 — vigesimal notation. A number splits into a high place (how many whole 20s it contains) and a low place (whatever is left over), exactly the same structural idea as tens and ones in decimal counting, just resting on a bigger group size. The high place comes from dividing by 20 and dropping the remainder; the low place is what's left once those groups of 20 are removed.
The leading explanation for why 20 was chosen at all is refreshingly physical: counting on both hands AND both feet gives twenty digits total, a natural stopping point before a number needs a second symbol. It's the same reasoning that likely gave decimal counting its own base of 10, just extended one step further to the toes.
This site also has a companion page converting into the Babylonian base-60 system, which splits a number the same structural way but around a completely different-sized group — comparing the two side by side shows that neither base 10, base 20, nor base 60 is somehow more 'natural' than the others; each is simply what one civilization settled on.
- Enter a whole number from 0 to 399 into the Decimal number field.
- Read the High place: the count of full 20s contained in that number.
- Read the Low place: whatever remains once those 20s are removed.
- Multiply the high place by 20 and add the low place to confirm you land back on the original number.
Worked example — converting 47
The decimal number 47 divided by 20 gives 2 whole groups of 20 (that's 40), with 7 left over — so its Mayan digits are high place 2 and low place 7. Checked in reverse: 2×20+7 = 47, exactly the starting number.
The largest number expressible with just these two places is 399 (19 full 20s plus a remainder of 19, since 20×20−1=399) — one short of needing a third place, the same way 99 is the largest two-digit value before ordinary decimal counting needs a third column.
Questions
Why did the Maya count in base 20?
The leading explanation is anatomical: counting on both hands and both feet gives twenty total digits, a natural group size before running out and needing a second symbol — the same logic that likely gave decimal counting its own base of 10, one step further along.
What's the largest number this calculator can convert?
399 — the largest value expressible with exactly two base-20 places (19×20+19). Higher values would need a third digit, the same way a third decimal digit becomes necessary once a count passes 99.
Did the Maya have a symbol for zero?
Yes, and notably earlier and more fully than several Old World number systems — Mesoamerican mathematics used a dedicated zero placeholder as a genuine working digit within its positional system, an important piece of mathematical history in its own right.
How is this different from the Babylonian Numbers page on this site?
Both split a decimal number into a high and low place using identical division-and-remainder logic, but this page groups by 20 while the Babylonian page groups by 60 — two civilizations, arrived at independently, settling on very differently sized groupings.
Was the Mayan number system used only for counting objects?
No — it was also central to their calendar systems, which combined multiple cycles of days and years, and vigesimal arithmetic underpinned the date calculations those calendars required.