Maya Numerals (Base 20) Converter — Vigesimal Dot-and-Bar Numbers
Convert any non-negative integer to and from Maya numerals — the ancient base-20 (vigesimal) system written with dots, bars and a shell zero. Type a decimal number to see its stacked dot-and-bar glyphs, place values and comma notation, or paste comma notation to read the decimal back. Live, in your browser.
How to Use
- Type a non-negative whole number in the Decimal box — the Maya glyphs, place values and comma notation update instantly.
- Or switch the input to Maya comma notation (e.g. <code>1, 5</code>) and type the base-20 digits to read the decimal value back.
- Read the stacked glyphs from the top place down: each level is a digit 0–19 drawn as bars (5 each) with dots (1 each) above, or a shell for zero.
- Click any value or its Copy button to copy it.
Maya places run high → low, separated by commas: 1, 0, 19 = 1×400 + 0×20 + 19×1 = 419.
Counting in twenties, with dots and bars
The Maya civilisation of Mesoamerica wrote numbers in base 20 — the vigesimal system — using a beautifully economical set of marks. A dot is worth 1, a bar is worth 5, and a stylised shell stands for zero — one of the earliest uses of a true zero anywhere in the world. Any single digit from 0 to 19 is built from at most three bars (15) and four dots (4): the digit 13, for instance, is two bars stacked under three dots, and 7 is one bar under two dots. This converter draws those glyphs for you and shows the matching place values and comma notation, both directions, live in your browser.
How positional base-20 works
Just like our decimal columns are worth ×1, ×10, ×100…, the Maya columns are worth ×1, ×20, ×400, ×8000…, written vertically with the largest place at the top. To convert a decimal number you divide repeatedly by 20 and read the remainders from the bottom up — each remainder (0–19) becomes one stacked digit. So 25 = 1×20 + 5×1, written 1, 5; and 400 = 1×400 + 0×20 + 0×1, written 1, 0, 0. To go the other way, multiply each digit by its place value and add. We write the digits here in comma notation — one number per place, highest first — which is the standard way scholars transliterate Maya stacks into text.
A note on the calendar
You may have read that the Maya system is “base 18” somewhere. That applies only to the Long Count calendar, where the third place counts ×360 rather than ×400 (because 18×20 = 360 days approximated a year). That is a calendar-specific modification. For ordinary arithmetic the Maya used a pure, consistent base 20, and that is exactly what this tool implements — every place is simply twenty times the one below it.
Quick reference
About the Maya Numerals (Base 20) Converter — Vigesimal Dot-and-Bar Numbers
Whether you are at a desk or on your phone, the Maya Numerals (Base 20) Converter — Vigesimal Dot-and-Bar Numbers makes everyday tasks easy — and it is completely free. Convert any non-negative integer to and from Maya numerals — the ancient base-20 (vigesimal) system written with dots, bars and a shell zero. Type a decimal number to see its stacked dot-and-bar glyphs, place values and comma notation, or paste comma notation to read the decimal back. Live, in your browser.
How it works
Type a value, then pick what you want to change it into. The answer appears straight away. It all happens on your own device, so it is fast and nothing you type is sent away. Just check that you picked the right “from” and “to” so you get the answer you wanted.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
How do Maya numerals work?
The Maya wrote numbers in base 20 (vigesimal) using just three marks: a dot worth 1, a bar worth 5, and a shell-shaped glyph for zero. A single digit 0–19 is built from up to three bars and up to four dots — for example 13 is two bars (10) plus three dots (3). Multi-digit numbers are stacked vertically, with the highest place value at the top.
What are the place values?
In pure base-20 each place is 20 times the one below it: the bottom row counts ×1 (the units), the next ×20, then ×400, ×8000 and so on. So the stack “1, 0” means 1×20 + 0×1 = 20, and “1, 0, 0” means 1×400 = 400.
Why did the Maya use base 20?
Most likely because of finger-and-toe counting — twenty digits on the human body. Vigesimal systems appear in several Mesoamerican cultures, and traces survive in languages such as French (quatre-vingts, “four twenties”, for 80) and older English (“three score”).
Isn’t the Maya calendar base 18 in one place?
The Long Count calendar used a modified system: the third place counted ×360 instead of ×400, because 18×20 = 360 approximated a year. That tweak is specific to dates. This converter uses the clean, purely positional base-20 system (×1, ×20, ×400, ×8000…) so the arithmetic stays consistent.
Is anything uploaded?
No. The whole conversion runs in your browser with JavaScript — nothing is sent to a server.
How do I use the Maya Numerals (Base 20) Converter — Vigesimal Dot-and-Bar Numbers?
Just type or paste your value. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Teaching number systems
Show students a real non-decimal, non-binary base used for centuries — and let them build numbers from dots and bars.
Maya archaeology & epigraphy
Sanity-check a transcribed glyph stack against its decimal value, or render a value to compare with an inscription.
Games, art & tattoos
Render a year, date or lucky number as authentic dot-and-bar glyphs for designs, props or worldbuilding.
Understanding place value
Base 20 makes the idea of positional notation concrete: the same digit means a different amount depending on its row.
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