Counting has always accompanied humanity, from the first tally marks to modern mathematics. Take a dive into the history of numbers with our Mayan numerals converter! Here you will learn a couple of things about numbers, (almost) everything about the Mayan numeral system, how to convert Mayan numerals — with our tool or by yourself — how our converter works, and how to add and subtract Mayan numeral symbols. Ready?
A short history of numbers
Counting is more widespread than we usually think, and many animal species are pretty good at simple math! We humans are no exception: since the time of our great-great-…-great-grandmas, our species evolved a deep understanding of that field — just ask the Egyptians with their Egyptian fractions.
Nowadays, Arabic numerals are the most used around the world. Easy to understand, with space for a decimal separator and a placeholder (0), they quickly overtook other systems. Fun fact: Arabic numerals actually come from India!
A fundamental feature of any numeral system is the base: the number of numerals used to represent any number. For the Arabic numeral system the base is 10:
1, 2, 3, 4, 5, 6, 7, 8, 9, 0
The fact that 10 is usually also the number of fingers on your hands 🖐🖐 is no coincidence — base-10 makes counting on your hands easier. However, many other bases exist. The device you are reading on right now operates in base-2 (using only 1s and 0s), Babylonians used base-60 (which is why there are 60 minutes in an hour), and various cultures used base-20.
The Mayan numeral system
The Maya were one of the cultures using base-20 (a vigesimal system). They were pretty good at math, and their calendars — used for astronomical purposes — are exquisitely accurate. The Mayan numeral symbols use a combination of dots and bars (lines), plus the representation of a seashell for 0.
- A dot is worth 1.
- A horizontal bar is worth 5 (it corresponds to 5 dots).
- A seashell represents 0.
Numbers from 0 to 19 are represented by stacking dots (up to four) above bars (up to three). After 19, it is necessary to use the powers of 20 to build bigger numbers. Numbers bigger than 19 are constructed by taking the numerals corresponding to the successive powers of 20 and putting them one over the other. We start with the numeral for the zeroth power (20⁰ = 1) at the very bottom and go upwards, so higher numerals correspond to higher powers of 20.
Example: reading a Mayan number
Consider a number made of two numerals. The higher numeral (3 bars and 2 dots) is worth 5×3 + 2 = 17, and the lower numeral (4 dots) is just 4. Now let the powers of 20 do their job:
17 × 20¹ + 4 × 20⁰ = 340 + 4 = 344
That's it! The cute stacked symbol equals what we now understand as 344.
How to convert Mayan numerals from Arabic numerals
Take a number — any number, as big as you like — and follow these steps:
- Divide the number by 20. Write down the remainder.
- Take the integer quotient from the previous operation and divide it again by 20. Write down the remainder.
- Follow the steps until the integer quotient is 0.
The series of remainders (read from last to first) is the number written in base-20. Let's try this method with 3,193,619:
| Division | Integer quotient | Remainder (base-20 digit) |
|---|---|---|
| 3,193,619 / 20 | 159,680 | 19 |
| 159,680 / 20 | 7,984 | 0 |
| 7,984 / 20 | 399 | 4 |
| 399 / 20 | 19 | 19 |
| 19 / 20 | 0 | 19 |
Reading the remainders from bottom to top, the base-20 representation of 3,193,619 is [19] [19] [4] [0] [19]. Each of those positions is then drawn with dots, bars, and a shell (for the 0), stacked highest power on top.
How to add and subtract using the Mayan numeral system
Because the system is positional, arithmetic works just like it does with our numbers — you just carry (or borrow) in groups of 20 instead of groups of 10.
- Addition: add the dots and bars in each position. If a position reaches 5 dots, replace them with 1 bar. If a position reaches 20 (four bars), remove those 20 units and carry 1 dot to the position above (the next power of 20).
- Subtraction: subtract position by position. If a position doesn't have enough units, borrow 20 from the position above (turn 1 unit of the higher power into 20 units below).
The fastest way to check any Mayan sum or difference is to convert both numbers to Arabic with the tool above, do the arithmetic in base-10, and convert the answer back to Mayan.
How to use our Mayan numerals converter
- Choose the conversion direction: Arabic → Mayan or Mayan → Arabic.
- For Arabic → Mayan, type any whole number (0 or greater). The tool shows the visual Mayan symbol (dots, bars, and shell), the base-20 digits, and a positional breakdown.
- For Mayan → Arabic, type the value of each Mayan position (0–19) separated by commas, from the highest power on top to the lowest at the bottom — for example
17, 4gives 344. - Read the results: the visual representation, the digit sequence, the place-value table, and the full formula.
Frequently Asked Questions
What base did the Maya use?
The Maya used a base-20 (vigesimal) positional system. Historians believe this comes from counting on both fingers and toes. Each position is worth 20 times the position below it: 1, 20, 400, 8,000, and so on.
How is zero written in Mayan numerals?
Zero is written as a stylized seashell (or shell) glyph. The Maya were one of the first civilizations to use a true symbol for zero as a placeholder, which is essential for a positional number system.
What do the dots and bars mean?
A single dot equals 1 and a horizontal bar equals 5. Within a single position you can have up to four dots (4) and up to three bars (15), which combine to represent any value from 0 to 19 before you move to the next power of 20.
Why is the Mayan calendar system related to base-20?
Mayan calendrical counts (like the Long Count) are closely tied to their vigesimal numerals, though the calendar introduces one irregular step (18 instead of 20) at the third position to align with the 360-day year. Our converter uses the pure mathematical base-20 system, not the calendar variant.
Can I convert very large numbers?
Yes. The converter handles whole numbers up to two billion, producing as many base-20 positions as needed. Each extra position simply multiplies the place value by another factor of 20.