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Mayan numerals used a base-20 (vigesimal) positional system — meaning each position's place value is a power of 20, the same way our familiar decimal system uses powers of 10 — represented visually with dots worth 1 each, horizontal bars worth 5 each (so up to four dots and up to three bars combine to write any single digit from 0 to 19), and a distinctive shell-glyph symbol representing zero. Remarkably, the ancient Maya independently developed the concept of a placeholder zero centuries before it reached Europe, making their number system one of the earliest recorded uses of positional zero anywhere in the world. This converter is a genuine mathematical curiosity and an educational tool for exploring how different base systems and positional notation work.
How it works
Choose a direction. For decimal to Mayan, enter a whole number; the calculator repeatedly divides by 20 (the standard technique for converting any number into a different base), recording each remainder from least significant to most significant, then describes each resulting base-20 digit (0-19) as its dot-and-bar representation (or the zero shell, if that digit is 0). For Mayan to decimal, enter the base-20 digits as a comma-separated list (most significant digit first, each between 0 and 19), and the calculator multiplies each digit by its corresponding power of 20 (1, 20, 400, 8000, ...) and sums the results.
- Enter conversion direction.
- Enter decimal number (decimal → Mayan).
- Enter mayan base-20 digits, comma-separated (Mayan → decimal).
- Click Calculate to see your results.
Examples
Decimal 429
429 ÷ 400 = 1 remainder 29; 29 ÷ 20 = 1 remainder 9. So 429 = 1×400 + 1×20 + 9, giving base-20 digits [1, 1, 9]. The final digit, 9, is shown as 1 bar (5) plus 4 dots (4×1=4), totaling 5+4=9.
Decimal 7385
7385 ÷ 400 = 18 remainder 185; 185 ÷ 20 = 9 remainder 5. So 7385 = 18×400 + 9×20 + 5, giving base-20 digits [18, 9, 5]. Checking: 18×400=7200, 9×20=180, plus 5, totals 7200+180+5=7385. The digit 18 is shown as 3 bars (15) plus 3 dots (3), the digit 9 as 1 bar plus 4 dots, and 5 as exactly 1 bar with no dots.
Mayan digits [1, 0] back to decimal
This represents 1×20 + 0×1 = 20 — a single dot in the 20s place, with the zero shell glyph in the 1s place.
Who should use it
- Exploring how different positional number systems and bases work.
- History-of-mathematics coursework on the Maya numeral system.
- Verifying a base-20 conversion by hand for a school project.
Industry applications
- Mathematics and history education
Advantages
- Converts accurately in both directions using a consistent base-20 system.
- Illustrates the historically significant early use of a placeholder zero.
Limitations
- Doesn't replicate the Maya Long Count calendar's modified base for its second position.
Common mistakes to avoid
- Entering a base-20 digit of 20 or more, which isn't a valid single digit in base 20 — anything reaching 20 must carry into the next position instead.
- Assuming this matches the Maya Long Count calendar exactly — the calendar's second position uses a multiplier of 18, not 20, which this general-purpose converter doesn't replicate.
- Forgetting that base-20 digits are entered most-significant-first, the same left-to-right order used when writing a decimal number.
Best practices
- Double check the direction (decimal-to-Mayan or Mayan-to-decimal) is set correctly before entering your value.
- When converting Mayan to decimal, verify each entered digit is between 0 and 19 before submitting.
- Use the repeated-division-by-20 technique to manually verify a decimal-to-Mayan conversion if you want to check the tool's result by hand.
Tips
- Curious about other historical or alternative-base number systems? Look for a Roman Numerals or Binary/Hex Converter alongside this tool.