Mayan Numerals — Vigesimal Legacy
Convert between decimal and base-20. The Maya invented one of the first positional zero symbols. Long Count, Tzolkin, and Haab calendars use vigesimal.
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13.0.0.0.0 (Dec 21, 2012) marked end of a 5,126-year cycle. Maya invented one of the first positional zero symbols (shell glyph). Tzolkin = 260 days; Haab = 365 days.
Ready to run the numbers?
Why: Mayan numerals powered the Long Count calendar and Mesoamerican astronomy. Base-20 may derive from fingers and toes.
How: Divide by 20 repeatedly for decimal→Mayan; multiply each digit by 20^position and sum for Mayan→decimal. Use commas for vigesimal digits.
Run the calculator when you are ready.
Mayan Numerals — Base-20 & the Long Count
Convert between decimal and vigesimal notation. Explore the Maya concept of zero, the Long Count calendar, and why 13.0.0.0.0 mattered in 2012.
Conversion Direction
Input Value
For educational and informational purposes only. Verify with a qualified professional.
🧮 Fascinating Math Facts
13.0.0.0.0 (Dec 21, 2012) marked end of a 5,126-year cycle in the Long Count
— Calendar
Maya invented one of the first positional zero symbols (shell glyph) in the Americas
— Math History
📋 Key Takeaways
- • Mayan numbers use base-20 (vigesimal)
- • Digits 0–19: dots (•) for 1–4, bars (—) for 5, shell (⬜) for 0
- • Long Count: baktun, katun, tun, uinal, kin (20^4, 20^3, 20^2, 20^1, 20^0)
- • Tzolkin = 260 days; Haab = 365 days
- • Maya invented one of the first positional zero symbols in the Americas.
💡 Did You Know?
📖 How It Works
Decimal→Mayan: divide by 20 repeatedly, collect remainders. Mayan→Decimal: multiply each digit by 20^position and sum. Use commas to separate vigesimal digits (e.g., 18,5 = 365).
🎯 Expert Tips
💡 Comma-Separated
Mayan notation: 13,0 or 1,9,4
💡 Digits 0–19
Each position holds 0–19
💡 Long Count
13,0,0,0,0 = 1,872,000 days
💡 Zero
Maya had a shell symbol for zero
⚖️ Comparison Table
| Decimal | Mayan |
|---|---|
| 20 | 1,0 |
| 365 | 18,5 |
| 260 | 13,0 |
| 7200 | 1,0,0,0 |
❓ Frequently Asked Questions
Why base-20?
Maya used fingers and toes (20 digits) for counting. Some variants used 18 in the third position (360 ≈ solar year).
What is the Long Count?
A linear count of days from a creation date. 13.0.0.0.0 = 1,872,000 days ≈ 5,125 years.
Tzolkin vs Haab?
Tzolkin = 260 days (sacred). Haab = 365 days (solar). Combined in Calendar Round.
Did Maya have zero?
Yes. One of the first civilizations with a positional zero (shell symbol).
How does vigesimal compare to decimal?
Base-20 uses fewer digits for large numbers but each digit has more possible values (0–19 vs 0–9).
📊 Key Stats
📚 Reference Sources
⚠️ Disclaimer: Educational tool. For scholarly research, consult academic sources. Long Count variants exist.
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