Mayan Numerals Converter: Numbers to Maya Dots and Bars and Back
Convert any whole number to Maya numerals (dots, bars and the shell zero) and back, in pure base 20 or the Long Count 18 × 20 system, with the division steps.
How it works
Pure base 20: N = d₁ + d₂×20 + d₃×400 + d₄×8,000 + … (dₖ = 0–19, level 1 at the bottom) · Long Count: N = d₁ + d₂×20 + d₃×360 + d₄×7,200 + d₅×144,000 + … (d₂ = 0–17) · digit symbol: d = 5 × bars + dots, shell = 0 · converting: divide by 20 repeatedly (by 18 for the second step in the Long Count) and read the remainders upwards
The Maya wrote numbers with three symbols: a dot for 1, a bar for 5 and a shell for 0. One level holds a digit from 0 to 19 (up to three bars and four dots, dots on top), and levels are stacked vertically so each level is worth 20 times the one below it: 1, 20, 400, 8,000 and so on. To convert a number, divide it by 20 again and again; the remainders, read from the last to the first, are the levels from the top down. To read a Maya numeral, multiply each level by its place value and add. The Long Count calendar, which counted days, made one change: the third level is worth 18 × 20 = 360 instead of 400, so the second level (winal) only goes up to 17 and the higher levels are 7,200 (kʼatun) and 144,000 (bʼakʼtun). Choose “Long Count” to use those place values, as the known large numbers in Maya inscriptions do. Results include the dot-and-bar symbols for every level (🐚 marks the shell zero), the expanded form, the same number in the other system and the division steps. The Roman numeral converter does the same job for Roman numbers, and the Mayan calendar converter turns Long Count dates into calendar dates; this page converts plain numbers.
Worked example
Convert 2026 in pure base 20. 2,026 ÷ 20 = 101 remainder 6, so the bottom level is 6 (one dot over one bar). 101 ÷ 20 = 5 remainder 1, so the second level is 1 (one dot). 5 ÷ 20 = 0 remainder 5, so the top level is 5 (one bar). Reading top to bottom the Maya digits are 5.1.6: 5 × 400 + 1 × 20 + 6 × 1 = 2,000 + 20 + 6 = 2,026. In the Long Count the same number is 5.11.6, because 5 × 360 + 11 × 20 + 6 = 2,026.
Sources: Wikipedia: Maya numerals (symbols, base 20, Long Count 18 × 20) · Omni Calculator: Mayan numerals converter (344 and 3,193,619 examples) · PlanetCalc: Maya numerals (pure and modified Long Count system)
Frequently asked questions
How do you write numbers in Mayan numerals?
Up to 19, use one level: a bar for each 5 and a dot for each 1 left over, dots above bars. 13 is two bars and three dots. From 20 on, stack levels worth 1, 20, 400, 8,000…: 52 = 2 × 20 + 12, so it is two dots on top of two bars and two dots.
What is 2026 in Mayan numerals?
In pure base 20, 2026 = 5 × 400 + 1 × 20 + 6, written as a bar (5) on top, a dot (1) in the middle and one dot over one bar (6) at the bottom: 5.1.6. With Long Count place values it is 5.11.6.
How did the Maya write zero?
With a shell-shaped glyph. The Maya were among the first peoples to use a true positional zero: Long Count dates from as early as 36 BC imply it, and inscriptions that actually show the zero glyph survive from the 3rd century AD onwards. The shell fills an empty level, as in 20 = one dot above a shell.
Why is the Maya third place 360 instead of 400?
In the Long Count calendar 18 winal of 20 days make one tun of 360 days, close to a solar year. So the second level only goes up to 17 and the third is worth 360. Everyday counting is thought to have used pure base 20 (400), but the surviving large numbers are calendar counts that use 360.
How do I read a Maya numeral?
Find the value of each level (5 per bar, 1 per dot, 0 for a shell), then multiply from the bottom by 1, 20, 400, 8,000… and add. For three bars and two dots above four dots: 17 × 20 + 4 = 344.
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