Mayan numerals

Published junio 8, 2026 · By NumberWiki

The vigesimal (base 20) positional number system used by the Maya civilisation of southern Mexico, Guatemala, Belize, and Honduras. Built from three symbols — a dot, a bar, and a stylised shell for zero — and in use from at least the third century BCE through the Spanish conquest of the sixteenth century CE.

Three symbols, twenty digits

Mayan numerals build all twenty digits (0 through 19) from a tiny visual vocabulary:

A dot (•) is one. Up to four dots in a row write the digits one through four.
A bar (▬) is five. One bar with zero to four dots above it writes five through nine; two bars give ten; three bars plus four dots give nineteen.
A shell (𝋠 in Unicode) is zero — a stylised conch with a cross-hatched interior, instantly recognisable across the surviving Maya corpus.

The Unicode Mayan Numerals block U+1D2E0–U+1D2F3 provides a precomposed glyph for each of the twenty digits, so we can render them as live text: 𝋠 𝋡 𝋢 𝋣 𝋤 𝋥 𝋦 𝋧 𝋨 𝋩 𝋪 𝋫 𝋬 𝋭 𝋮 𝋯 𝋰 𝋱 𝋲 𝋳. That is zero through nineteen, in order. (As with cuneiform and hieroglyphic numerals, you need a font with Mayan Numerals coverage installed to see the glyphs rather than boxes — Noto Sans Mayan Numerals is the standard free option.)

Stacking up, not writing across

Mayan numbers are positional, but the stacking convention is vertical, not horizontal. The largest place sits at the top of a column, smaller places descend beneath it. A two-place number like twenty (one × 20 + zero) is written as a dot above a shell:

𝋡
𝋠

That two-glyph vertical column is twenty. Three hundred (one × 20² + zero × 20 + zero) would be three glyphs stacked: dot, shell, shell. The Maya wrote numbers this way in their codices — folded bark-paper books — and carved them this way on stelae, lintels, and altars across the southern lowlands.

The Long Count irregularity

In one important application — the Long Count calendar used by the Classic Maya to date events relative to a base date in 3114 BCE — the positional system is modified at the second place. Instead of the third position being worth 20² = 400, it is worth 18 × 20 = 360, so that a full "round" of the third place corresponds approximately to a solar year. Higher places then go back to multiplying by 20 each.

The result is a hybrid notation: pure base 20 for everyday counting and merchant arithmetic, but a tweaked base-20-with-a-360-day-year for calendar dates. This is the system that produced the famous date 13.0.0.0.0 = December 21, 2012, which marked the end of one Long Count cycle of roughly 5,125 years — and which was widely (incorrectly) reported as a "Mayan prophecy" of world's end in the years leading up to that date. The Maya themselves treated the cycle rollover the same way we treat the rollover from December 31 to January 1: the calendar ticks over and starts the next cycle.

Why base 20?

Twenty is a natural counting base for a culture that counts on fingers and toes — and the Mayan and broader Mesoamerican languages preserve many traces of this. Yucatec Maya words for twenty (k'aal), for instance, are independent lexical items rather than constructions like "two tens." The pattern is widespread in vigesimal systems worldwide: pre-modern Basque, Welsh, Yoruba, Tlingit, Aztec/Nahuatl, and even the surviving French traces (quatre-vingts for 80) all show the same logic of counting in twenties.

Twenty also has six divisors (1, 2, 4, 5, 10, 20), which makes fractional arithmetic relatively clean — not as clean as Babylonian 60, but cleaner than decimal 10. And it pairs nicely with the calendar cycle of 260 days (the sacred tzolk'in) used across Mesoamerica for ritual scheduling.

The Mayan zero

The shell glyph for zero is one of the most historically significant features of the system. Independent of the Babylonian placeholder wedges and centuries earlier than the Indian zero that ultimately propagated to Europe through the Arab world, the Maya had a fully positional zero — a sign that could occupy any place in a number, that was understood as a digit alongside the others, and that was essential to the unambiguous expression of large numbers in the Long Count.

The earliest secure Long Count date carved with a shell zero is from the late first century BCE, on Stela 2 at Chiapa de Corzo in modern Mexico, with a Long Count date corresponding to 36 BCE. By the Classic period (roughly 250–900 CE) the zero is universal in monumental inscriptions across the Maya region. Whether it predates the Babylonian late-period placeholder or develops independently is debated; what is clear is that it is a fully independent invention — and that the Maya, alone among the great pre-modern numerical traditions, used zero as a real digit from very early on.

What survives, and what was lost

The vast majority of pre-Columbian Maya writing was destroyed in the century after Spanish contact, either through deliberate burning (most infamously by Bishop Diego de Landa in Maní, Yucatán, in 1562) or through the slow loss of literacy as missionary schooling replaced traditional scribal training. Of the bark-paper codices that were produced by the thousands, only four survive: the Dresden, Madrid, Paris, and (more recently authenticated) Grolier / Maya codices, named for the cities where they ended up in European libraries.

These four codices, together with the dated inscriptions on stelae and the painted vessels that have survived in tombs, give us everything we know about Mayan numerical practice. The Dresden Codex in particular contains extensive astronomical and calendrical tables — including accurate predictions of Venus and lunar cycles — that demonstrate the system was used for serious mathematical work, not only for date-keeping.

Reading Mayan numerals on this site

NumberWiki renders Mayan numerals on every number page from 1 up to 159,999 (20⁴ − 1). For typographic reasons the rendering on this site is horizontal — most-significant place on the left, separated by middle dots — rather than the traditional vertical stack. The codepoints used are the precomposed Unicode Mayan Numerals (U+1D2E0 through U+1D2F3).

Some examples:

1 — 𝋡
19 — 𝋳 (three bars and four dots)
20 — 𝋡·𝋠 (one in the 20s place, zero in the ones)
400 — 𝋡·𝋠·𝋠 (one × 20², zero, zero)

The first 31 numbers in Mayan (0–30)

Each tile links to that number's page. Watch the rollover at 20: dots and bars fill the first place 0–19, then 20 becomes a dot above a shell (1·0 in base 20).