Babylonian Numeral Converter
About Babylonian Numerals
The Babylonian numeral system was sexagesimal (base-60). It used cuneiform symbols on clay tablets.
Symbols: ▼ (1) and ◄ (10). Groups of these form digits 1-59.
Place Value: Groups are separated by spaces. The rightmost group is units (60⁰), the next left is 60¹, then 60², etc.
Example: ▼ ◄▼▼ represents (1 × 60¹) + (10 + 1 + 1 × 60⁰) = 60 + 12 = 72.
This converter uses space as the place separator and covers numbers up to 359,999.
Babylonian Numeral Calculator
How It Works
The calculator converts the Babylonian numerals to decimal, performs the calculation, and converts the result back to Babylonian.
Input format: Use ▼ for 1, ◄ for 10, and spaces between place value groups. Each group must represent a value from 1 to 59.
Results are limited to positive integers between 1 and 359,999. Division results are floored.
Babylonian Numeral Reference
Basic Symbols
| Symbol | Value |
|---|---|
| ▼ | 1 |
| ◄ | 10 |
These are combined additively within a place value group (up to 59).
Place Value (Base-60)
Groups of symbols represent digits (1-59) in a base-60 system. Spaces separate the groups (place values).
Rightmost group: × 60⁰ (× 1)
Next group left: × 60¹ (× 60)
Next group left: × 60² (× 3600)
...and so on.
Example: ▼ ◄▼▼ = (1 × 60¹) + (12 × 60⁰) = 60 + 12 = 72
Examples (1-59)
| Decimal | Babylonian |
|---|---|
| 1 | ▼ |
| 9 | ▼▼▼▼▼▼▼▼▼ |
| 10 | ◄ |
| 11 | ◄▼ |
| 23 | ◄◄▼▼▼ |
| 59 | ◄◄◄◄◄▼▼▼▼▼▼▼▼▼ |
Examples (> 59)
| Decimal | Babylonian | Calculation |
|---|---|---|
| 60 | ▼ | (1 × 60¹) |
| 61 | ▼ ▼ | (1 × 60¹) + (1 × 60⁰) |
| 70 | ▼ ◄ | (1 × 60¹) + (10 × 60⁰) |
| 135 | ▼▼ ◄▼▼▼▼ | (2 × 60¹) + (15 × 60⁰) |
| 3600 | ▼ | (1 × 60²) |
| 3671 | ▼ ▼ ◄▼ | (1 × 60²) + (1 × 60¹) + (11 × 60⁰) |