Maya Numerals
An ancient vigesimal (base-20) numeral system using dots and bars
About Maya Numerals
Maya numerals are a vigesimal (base-20) numeral system used by the Maya civilization of Mesoamerica. The system was one of the most sophisticated numeral systems in the ancient world and was used for astronomical calculations, calendar systems, and trade.
The Maya numeral system uses only three symbols: a dot (●) representing one, a horizontal bar (▃▃▃▃▃) representing five, and a shell symbol (ↂ) representing zero. Numbers are written vertically, with the bottom position representing ones, the next position representing twenties (20¹), then four hundreds (20²), eight thousands (20³), and so on. This positional notation system was one of the first to use the concept of zero.
Key Features:
- Uses only three symbols: dot (●) for one, bar (▃▃▃▃▃) for five, and shell (ↂ) for zero.
- Vigesimal (base-20) positional system - each position represents a power of 20.
- Written vertically from bottom to top, with each level representing a different power of 20.
- One of the first civilizations to use the concept of zero as a placeholder.
- Additive notation within each position - dots and bars are combined to represent values 0-19.
- Used for complex astronomical calculations, calendar systems, and mathematical operations.
- Each position can hold values from 0 to 19 before carrying over to the next position.
Formation Rules:
- Dots (●) represent ones - up to four dots can be used (1-4).
- Bars (▃▃▃▃▃) represent fives - each bar equals 5.
- Dots and bars are combined additively within each position (e.g., 7 = one bar + two dots).
- Zero is represented by a shell symbol (ↂ).
- Numbers are written vertically, with the lowest position at the bottom.
- Each position above represents 20 times the value of the position below it.
Further Reading:
Maya Numeral Table
Basic Symbols
| Symbol | Value | Description |
|---|---|---|
| ● | 1 | Dot - represents one |
| ▃▃▃▃▃ | 5 | Bar - represents five |
| ↂ | 0 | Shell - represents zero |
Units (0-19) - Single Position Values
These are the values that can be represented in a single position (ones place). Each position in the Maya system can hold values from 0 to 19.
| Value | Maya Numeral | Explanation |
|---|---|---|
| 0 | ↂ |
Zero (shell symbol) |
| 1 | ● |
1 dot |
| 2 | ●● |
2 dots |
| 3 | ●●● |
3 dots |
| 4 | ●●●● |
4 dots |
| 5 | ▃▃▃▃▃ |
One bar |
| 6 | ● ▃▃▃▃▃ |
One bar + 1 dot |
| 7 | ●● ▃▃▃▃▃ |
One bar + 2 dots |
| 8 | ●●● ▃▃▃▃▃ |
One bar + 3 dots |
| 9 | ●●●● ▃▃▃▃▃ |
One bar + 4 dots |
| 10 | ▃▃▃▃▃ ▃▃▃▃▃ |
Two bars |
| 11 | ● ▃▃▃▃▃ ▃▃▃▃▃ |
Two bars + 1 dot |
| 12 | ●● ▃▃▃▃▃ ▃▃▃▃▃ |
Two bars + 2 dots |
| 13 | ●●● ▃▃▃▃▃ ▃▃▃▃▃ |
Two bars + 3 dots |
| 14 | ●●●● ▃▃▃▃▃ ▃▃▃▃▃ |
Two bars + 4 dots |
| 15 | ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ |
Three bars |
| 16 | ● ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ |
Three bars + 1 dot |
| 17 | ●● ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ |
Three bars + 2 dots |
| 18 | ●●● ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ |
Three bars + 3 dots |
| 19 | ●●●● ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ |
Three bars + 4 dots |
Positional System Explanation
Maya numerals use a vigesimal (base-20) positional system. Each position represents a power of 20:
| Position (from bottom) | Power of 20 | Value Multiplier | Example |
|---|---|---|---|
| 1st (bottom) | 20⁰ | × 1 | Ones (0-19) |
| 2nd | 20¹ | × 20 | Twenties (0-19 × 20) |
| 3rd | 20² | × 400 | Four hundreds (0-19 × 400) |
| 4th | 20³ | × 8,000 | Eight thousands (0-19 × 8,000) |
| 5th | 20⁴ | × 160,000 | 160 thousands (0-19 × 160,000) |
Examples of Numbers:
| Value | Maya Numeral | Breakdown |
|---|---|---|
| 12 | ●● ▃▃▃▃▃ ▃▃▃▃▃ |
Single position (ones) |
| 85 | ●●●● ▃▃▃▃▃ |
4 × 20 + 5 |
| 153 | ●● ▃▃▃▃▃ ●●● ▃▃▃▃▃ ▃▃▃▃▃ |
7 × 20 + 13 |
| 999 | ●● ●●●● ▃▃▃▃▃ ●●●● ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ |
Multiple positions (vigesimal) |
| 1234 | ●●● ● ●●●● ▃▃▃▃▃ ▃▃▃▃▃ |
Multiple positions (vigesimal) |
| 12345 | ● ▃▃▃▃▃ ▃▃▃▃▃ ●● ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ |
Multiple positions (vigesimal) |
| 54321 | ● ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ ● ▃▃▃▃▃ ▃▃▃▃▃ ▃▃▃▃▃ ● |
Multiple positions (vigesimal) |
Larger Numbers:
| Value | Maya Numeral | Note |
|---|---|---|
| 20 | ● ↂ |
First power of 20 (20¹) |
| 40 | ●● ↂ |
Vigesimal representation |
| 100 | ▃▃▃▃▃ ↂ |
Vigesimal representation |
| 200 | ▃▃▃▃▃ ▃▃▃▃▃ ↂ |
Vigesimal representation |
| 400 | ● ↂ ↂ |
Second power of 20 (20²) |
| 800 | ●● ↂ ↂ |
Vigesimal representation |
| 1000 | ●● ▃▃▃▃▃ ▃▃▃▃▃ ↂ |
Vigesimal representation |
| 2000 | ▃▃▃▃▃ ↂ ↂ |
Vigesimal representation |
| 4000 | ▃▃▃▃▃ ▃▃▃▃▃ ↂ ↂ |
Vigesimal representation |
| 8000 | ● ↂ ↂ ↂ |
Third power of 20 (20³) |