Babylonian Numbers Converter
Convert between decimal and ancient Babylonian sexagesimal (base-60) numbers
Convert Babylonian Numbers
Conversion Results
Enter a valid number to see conversion results
Example Conversions
Decimal to Babylonian
Example: 13451 (decimal)
13451 ÷ 60 = 224 remainder 11
224 ÷ 60 = 3 remainder 44
3 ÷ 60 = 0 remainder 3
Result: 3.44.11 (Babylonian)
Babylonian to Decimal
Example: 12.9.35.0.22 (Babylonian)
12×60⁴ + 9×60³ + 35×60² + 0×60¹ + 22×60⁰
= 155,520,000 + 1,944,000 + 126,000 + 0 + 22
Result: 157,590,022 (decimal)
Babylonian Symbols
Units (1-9)
𒐕 = 1 (vertical wedge)
𒐕𒐕 = 2
𒐕𒐕𒐕 = 3
... up to 𒐕𒐕𒐕𒐕𒐕𒐕𒐕𒐕𒐕 = 9
Tens (10-50)
◁ = 10 (triangular wedge)
◁◁ = 20
◁◁◁ = 30
◁◁◁◁ = 40
◁◁◁◁◁ = 50
Special
⦻ = 0 (empty space/placeholder)
Babylonian Math Facts
Used base 60 (sexagesimal) system
Developed around 4000 years ago
Written on clay tablets with stylus
Zero appeared only in middle of numbers
Used cuneiform script
Influenced modern time (60 minutes, 60 seconds)
Understanding Babylonian Numbers
What are Babylonian Numbers?
Babylonian numbers are an ancient numeral system that used base 60 (sexagesimal) instead of our modern base 10 (decimal) system. Developed over 4,000 years ago in Mesopotamia, this system was used for astronomical calculations, commerce, and mathematics.
Why Base 60?
- •60 has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
- •Easy for fractions and division
- •Practical for astronomical observations
- •Suitable for trade and measurement
Conversion Process
Decimal to Babylonian
1. Divide by 60 repeatedly
2. Record remainders
3. Read remainders bottom to top
Babylonian to Decimal
1. Multiply each digit by 60^position
2. Sum all results
3. Rightmost position = 60⁰ = 1
Modern Legacy
We still use base 60 today for:
- • Time: 60 minutes, 60 seconds
- • Angles: 360° (6 × 60), 60 arc-minutes
- • Geographic coordinates