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.
Why This Mathematical Concept Matters
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.
- ●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.
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.
📜 Quick Examples — Click to Load
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.