Mayan Numerals Converter

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 Mayan numerals converter works; and
• How to add and subtract Mayan numeral symbols.

Ready?

Counting is more widespread than we usually think, and many animal species are pretty good at simple math! We (humans) are no exception, and since the time of our great-great-…-great-grandmas, our species evolved a deep understanding of that field: go ask the Egyptians with their Egyptian fractions! We are not sure whether it's a good thing or not, but young humans are the only ones wondering if they really need trigonometry in their lives.

Nowadays, Arabic numerals are the most used around the world. Easy to understand, with space for a decimal separator and a placeholder (0), it quickly overtook other systems. Fun fact: Arabic numerals actually come from India!

A fundamental feature of any numeral system is the base: the amount of numerals used to represent any number. For the Arabic numeral system, the base is 10:
$1, 2, 3, 4, 5, 6, 7, 8, 9, 0$

Now, the fact that 10 is usually also the number of fingers in your hands 🖐🖐 is not a 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), and through history, humans tried other bases. Babylonians used base-60, as we've seen in our Babylonian numbers converter, that's why there are 60 minutes in an hour; and various cultures used base-20.

If you want to learn something more about bases, check our other tools:

• Decimal to binary converter;
• Decimal to hexadecimal converter
• Binary to hexadecimal converter.

Mayans were one of the cultures using base-20. They were pretty good at math, and their calendars (used for astronomical purposes) are exquisitely accurate — although they didn't predict the end of the world in 2012; for them, it was only turning the pages of their calendars. We developed the Mayan calendar converter to give you a detailed explanation of their way to keep track of time.

The Mayan numeral symbols use a combination of dots and lines, plus the representation of a seashell for 0.
A line corresponds to 5 dots, and it prompts the beginning of a new line, right above the last one.
Numbers from 0 to 19 are represented in this way. After that, it is necessary to use the powers of 20 to build bigger numbers.

Numbers bigger than 19 are constructed in the Mayan system by taking the numerals corresponding to the successive powers of 20 and putting them one over the other. We start with the numeral corresponding to the zeroth power at the very bottom and go upwards; thus, higher numerals correspond to higher powers of 20.

The Mayan number that you can see in the picture above consists of two numerals — this means it uses the zeroth power of 20 and the first power of 20. The lower numeral (consisting of 4 dots) corresponds to the zeroth power, and the higher numeral (consisting of 3 lines and 2 dots) corresponds to the first power. Let's decode this number!
The higher numeral is equal to $5 × 3 + 2 = 17$ (because each line is worth 5 and each dot is worth 1) and the lower numeral is just $4$. Now let the powers of 20 do their job:

That's it! The cute number above is what we now understand as 344. How about going the other way round and finding the Mayan version of "our" numbers? Keep reading!

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 again by 20. Write down the remainder and…
• Follow the steps until the integer quotient is 0.

That's it! The series of remainders is the number written in the new basis. Let's try this method with an example.

Take the number $3,\!193,\!619$.

• $3,\!193,\!619/20 = 159,\!680$ with remainder $19$;
• $19,\!680/20 = 7,984$ with remainder $0$;
• $7,\!984/20 = 399$ with remainder $4$;
• $399/20 = 19$ with remainder $19$;
• $19/20 = 0$ with remainder $19$.

The base 20 representation for $3,\!193,\!619$ is $19\ 0\ 4\ 19\ 19$. It doesn't look good this way because we were using the digits of a decimal system. Let's see how it looks using Mayan numeral symbols.

You just learned how to convert Mayan numerals. Do you want to go a little bit deeper and learn how to calculate as if you were in Central America a couple of thousand years ago?

Let's try addition first. Take two Mayan numeral symbols, and then combine the symbols. Every 5 dots, remember to draw a line, and if you reach four lines, you have to add a dot in the higher position and use a seashell to represent the zero in place of the lines.

We choose 72 and 19. The dots in the lower numeral sum to 6: we then convert the 6 dots to 1 line and 1 dot. Then, there would be 6 lines: we combine 4 of them into a dot that gets moved to the numeral above.

Subtraction works in a similar way. Take two numerals and remove from the bigger one the symbols of the smaller one. If there are not enough dots, just trade a bar for five dots, and if there are not enough bars, remove one dot from the symbol right above and convert it into four bars in the symbol below (like borrowing them from the higher position).

Here we have 96 and 37. Let's start with the dots in the numeral below. There are too few of them in the first number, so we convert a line into 5 dots. Now we have 6 dots, and we subtract 2. Four dots remain on the right; does it check out?
Now, to the lines. Two in the first term (we removed one) and three in the second: we need to borrow a dot from the numeral above. The result on the left symbol is 3 dots above, and $4 + 2 = 6$ lines below. Now subtract the 3 lines of the right symbol, and you get the 3 lines of the result. Do the same with the dots of the higher numeral, and… you are done!

There's nothing easier in this world: simply insert the number you would like to convert and let us do all the divisions!

Remember not to use negative numbers! Archaeologists are not sure if Mayans used them!

If you want to exercise with addition and subtraction, our calculator can take input expressions such as $96−37$ and give you the result in Mayan symbols, so you can quickly check your result!

Now you know everything about counting and writing numbers like a Mayan!