What base did the Maya use?

The Maya used a base-20, or vigesimal, system — likely because people counted on fingers and toes. Each position in a Mayan number is worth 20 times the position below it, just as each decimal position is worth ten times the one to its right.

How are the digits 0 to 19 written?

Each Mayan digit combines dots and bars. A dot is worth 1 and a bar is worth 5, so a digit equals the number of bars times five plus the number of dots. For instance 13 is two bars and three dots. Zero is shown with a distinctive shell glyph.

Why is the Mayan zero significant?

The Maya independently invented a symbol for zero, the shell, centuries before it appeared in Europe. A true zero is what makes a place-value system work, because it marks an empty position rather than skipping it, allowing numbers like 400 to be written unambiguously.

How are positions arranged?

Mayan numbers are written vertically, with the most significant digit on top and the units position at the bottom. This converter shows the top row as the highest power of 20 and lists each row's contribution to the total.

Does this use the calendar Long Count rules?

No. The calendrical Long Count modifies the third position to 18 instead of 20 so a cycle equals 360 days. This tool uses the pure mathematical base-20 system, where every position is a clean power of 20, which is correct for ordinary arithmetic.

Mayan Numeral Converter

Write numbers the way the ancient Maya did

The Mayan Numeral Converter turns ordinary numbers into Maya numerals built from dots, bars and a shell for zero. The Maya counted in base 20, and their place-value system — complete with a genuine zero — was among the most sophisticated of the ancient world.

How it works

Converting a number to Mayan numerals is repeated division by 20:

while v > 0:
    digit = v mod 20   (a value 0..19)
    v = floor(v / 20)

Each resulting digit is rendered with the dot-and-bar rule: a digit equals bars × 5 + dots, so bars = floor(digit / 5) and dots = digit mod 5. Dots sit above bars within a position, and the positions stack vertically with the largest on top. A digit of zero is drawn as a shell.

Example

The year 2026 in base 20 is 5, 1, 6, because 5×400 + 1×20 + 6 = 2026. The top row is the digit 5 (one bar, no dots), the middle row is 1 (a single dot), and the bottom row is 6 (one bar plus one dot). The converter shows each row’s power-of-20 contribution adding up to 2026.

Notes

This tool implements the pure mathematical base-20 system where every position is an exact power of 20. The Maya calendar’s Long Count uses a special second-tier value of 18 to make a cycle equal 360 days; that variant is intentionally not used here so the arithmetic stays a clean vigesimal place-value system.