Babylonian Numbers Calculator

Math

Convert decimal numbers to and from the ancient Babylonian base-60 (sexagesimal) numeral system.

Formula

Decimal → base-60 by repeated division; each digit in range [0, 59]
  • Babylonians used base-60 (sexagesimal) — the origin of our 60-second minutes and 360° circles.
  • They used only two symbols: a vertical wedge (1) and a corner wedge (10).
  • This calculator shows the base-60 digits; each digit 0-59 would be represented by combinations of wedge marks.

3,661 in Babylonian

Inputs
  • Decimal Number: 3661

3661 = 1×60² + 1×60¹ + 1×60⁰ = digits: 1, 1, 1 (one hour, one minute, one second!)

Frequently asked questions

Why did Babylonians use base-60?
60 has many divisors (1,2,3,4,5,6,10,12,15,20,30,60) making fractions easy, which was valuable for astronomy and trade.
Why do we still use base-60?
Our time system (seconds, minutes, hours) and angle measurements (degrees) come directly from Babylonian mathematics.
What were the actual symbols?
A vertical wedge (▽) represented 1 and a corner wedge (◁) represented 10. Numbers 1-59 were combinations of these.
Did they have a zero?
Early Babylonians used a space for zero. By ~300 BCE they developed a placeholder symbol.