Mayan Numeral Calculator - Vigesimal Base-20 Conversion

A Mayan numeral calculator is a tool that translates a decimal value into the stacked dot, bar, and shell glyphs of the Maya vigesimal system. Type a number from 0 to 3,199,999 and the calculator shows the base-20 digit at each of the five levels. Each digit is 0 to 19, where 0 is the shell, 1 is a dot, and 5 is a horizontal bar.

• • Homework and puzzle solving: Confirm a base-20 conversion by hand against the calculator's level-by-level breakdown.
• • Calendar and archaeology studies: Explore how a Maya Haab year rounds through 18 months of 20 days plus a closing 5-day Uayeb period.
• • Encoding and study notes: Turn a year or date into a Maya glyph stack for a poster or notebook margin.
• • Number system drills: Practice reading positional numeral systems by switching between decimal, base-20, and base-2 in the same worksheet.

The Maya number system is a true positional system, so the meaning of each glyph depends on the level where it sits. The same three dots that mean 3 in the ones place mean 60 in the 20s place and 1,200 in the 400s place. The calculator therefore reports the dot, bar, and shell pattern and the level where each pattern lives, so the result reads the way a Maya scribe would have read it on a stela or in a codex.

For an additive-subtractive numeral system that uses seven letters, the Roman Numeral Converter reads the same 1 to 3,999 range and renders each value as a string of I, V, X, L, C, D, and M glyphs.

The calculator reads the decimal value, divides it by 20 repeatedly, and writes each remainder as a Maya digit at the next level of the stack, from the bottom 1s place up to the topmost 160,000s place.

• value: The decimal integer you enter, clamped to the range 0 to 3,199,999 so all five base-20 levels stay available.
• d1 to d5: The base-20 digit at levels 1 to 5, where d1 is the top of the stack (160,000s) and d5 is the bottom (1s).
• digitCount: The number of levels that hold a non-zero digit, between 1 and 5; the ones place is always shown.

The conversion runs in a single pass: each division by 20 peels off the next digit from the bottom, and the stack is built from the last remainder up to the first. Because the result uses full integer arithmetic, the digits are exact at every boundary from 19 to 3,199,999, with no rounding loss.

According to Smithsonian National Museum of the American Indian, the Maya number system is a base-20 (vigesimal) positional system in which a single dot represents 1, a horizontal bar represents 5, and a shell or oval glyph represents 0.

To translate the same decimal value into binary, octal, hexadecimal, or any other base, the Base Converter applies the same repeated-division algorithm and reports the matching place values.

Four short ideas cover the symbols, the base, the place values, and the zero placeholder that the Maya number system is built on.

These four ideas are the backbone of every Maya numeral. Once a student can read 7 as one bar and two dots, the rest of the system is just a question of which level the glyph sits on. The shell is the only true zero placeholder that survives in modern Mayan languages, and the same idea shows up in modern positional systems like decimal and binary.

For the same idea applied to base-2, base-8, and base-16 positional systems, the Change of Base Calculator walks through the change-of-base step and lists the place values for each level.

Type a decimal value, then read the matching Maya glyph stack and the base-20 digit at every level.

1. 1 Enter a decimal value: Type a whole number from 0 to 3,199,999 in the input field; the calculator clamps out-of-range and non-integer values to the nearest valid whole number.
2. 2 Read the Maya glyph stack: The result panel prints the five levels from the 160,000s place at the top to the 1s place at the bottom, with each level showing the dot, bar, and shell glyph that represents its base-20 digit.
3. 3 Read the digit at every level: The secondary result list shows the base-20 digit value from 0 to 19 for level 1 through level 5, so you can read the same stack as a list of five numbers.
4. 4 Check the active level count: The active level count tells you how many levels the stack actually uses, between 1 and 5, so a small number like 7 does not look empty.
5. 5 Try a boundary value: Change the input to 20, 400, 8,000, or 160,000 to see the stack grow by one level each time the value crosses a new place-value threshold.
6. 6 Reset and try a new value: Use the Reset button to restore the default value of 1,234 and start a fresh conversion without retyping the input.

Suppose you want to translate the year 2025 into a Maya glyph stack. Enter 2025 in the input field; the calculator reports the active level count as 3, with the level 3 digit equal to 5 (400s place), the level 4 digit equal to 1 (20s place), and the level 5 digit equal to 5 (1s place). The glyph stack shows a single bar at the 400s level, a single dot at the 20s level, and a single bar at the 1s level.

To translate the same input into the base-2 version of the same positional idea, the Binary Converter lists the binary digits at the matching power-of-2 levels.

A short list of why a calculator is useful when you are learning the Maya number system.

• • Visual reading of Maya glyphs: Stacks dots, bars, and a shell into a text block, so the result reads the way a Maya stela or codex would read.
• • Level-by-level digit list: Reports the base-20 digit at every one of the five levels, so the same result works as a clean base-20 list for a worksheet or a quiz.
• • Handles the full 5-level range: Supports values from 0 to 3,199,999, the largest value that fits in five base-20 levels.
• • Real-time updates as you type: Updates the result panel every time the input changes, so you can experiment with 20, 400, 8,000, and 160,000 in seconds.
• • Highlights the ones place: Lists the level 5 digit separately, which is the digit students need to read first when checking a conversion by hand.

For a teacher, the Mayan numeral calculator is a quick way to confirm a class answer key without redoing the layout. For a student, the level-by-level digit list is the most reliable way to learn that 14 in the ones place is the same pattern as 14 in the 20s place; only the level changes, the glyph does not.

To read the same input in plain English words in addition to the Maya glyph stack, the Number to Words Converter spells out the decimal value digit by digit.

The decimal input is the only thing that changes the result, but the place values and the calendar variation are easy to mix up when you are reading a Maya number for the first time.

• • The calculator uses the pure mathematical base-20 (vigesimal) system at every level, not the calendar-modified version where the third level is 360 days instead of 400; a Haab calendar year would need a separate tool.
• • The output is rendered with Unicode dot, bar, and shell characters in a text block; the visual layout is text-based rather than a hand-drawn Maya stela.

If a number comes from a Maya codex or a Haab calendar, the third level may be 360 instead of 400. A pure mathematical number like 1,234 always uses 400 at the third level, and the calculator reports that pure mathematical version, so the digit list matches what a modern base-20 mathematician would write, not what a Maya calendar keeper would write.

According to Britannica, the Maya used a vigesimal (base-20) positional system with a dot for 1, a bar for 5, and a shell for 0, and they wrote numerals vertically with the largest place value at the top.

Per MacTutor History of Mathematics, the Maya numerals use a dot for 1, a bar for 5, and a shell for 0, and they stack vertically in base-20 levels of 1, 20, 400, 8,000, and 160,000 with the largest place value at the top.