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