Sumerian Board
Free Sumerian Board for math. Enter values to solve step-by-step with verified formulas, worked examples, and detailed explanations. Free math tool.
Formula
Value = (Col3 × 3600) + (Col2 × 60) + Col1
Positional system based on powers of 60. Columns accumulate values up to 59 before carrying over.
Worked Examples
Example 1: Number 70
Problem:70 in Base 60
Solution:70 = 60 + 10. 1 in the 60s column. 10 in the 1s column.
Result:1, 10
Frequently Asked Questions
What is the Sumerian number system?
The Sumerians (and later Babylonians) used a base-60 (sexagesimal) system. It originated around 3000 BCE and is the reason we have 60 seconds in a minute and 360 degrees in a circle.
How does Base-60 work?
Like our decimal system uses powers of 10 (1, 10, 100), sexagesimal uses powers of 60 (1, 60, 3600). A number in the second column is multiplied by 60.
What are the tokens?
Early Sumerians used clay tokens. A small cone represented 1, a small ball represented 10, a large cone 60, and a large cone with a hole 600. Sumerian Board simplifies this into a positional board.
Did they have a zero?
Initially, no. They used a space to indicate an empty place value. Later Babylonians developed a placeholder symbol (two slanted wedges), but it wasn't a true zero number as we know it, just a separator.
How did they perform calculations?
They used counting boards with tokens or drew lines in the sand. They also had extensive reference tables for reciprocals, squares, and cubes written on clay tablets to assist with division and multiplication.
What is Cuneiform?
Cuneiform is the wedge-shaped writing system used by Sumerians. They pressed a reed stylus into soft clay. Our numbers use standard Cuneiform symbols: a vertical wedge (v) for 1 and a corner wedge (<) for 10.
How do I convert decimal to Sumerian?
Divide the decimal number by 60 repeatedly. The remainders become the digits in each column, reading from right (units) to left (60s, 3600s).
What is the difference between Sumerian and Babylonian math?
Sumerian math laid the foundation with the base-60 system and tokens. Babylonian mathematicians (who came later in the same region) refined this into a fully positional system and developed advanced algebra and geometry.
Background & Theory
The Sumerian system is positional sexagesimal (Base 60).
Place Values:
- Right column (Dish): $60^0$ (Values 1-59)
- Middle column (Gesh): $60^1$ (Values 60-3540)
- Left column (Shar): $60^2$ (Values 3600-215999)
Within a Column:
It functions additively (base 10 sub-base).
- ▼ (Vertical Wedge): Value 1.
- ◀ (Corner Wedge): Value 10.
- Values up to 59 are formed by grouping these wedges (e.g., 23 is ◀◀▼▼▼).
Example:
The number 75 is written as [1, 15].
1 × 60 + 15 × 1 = 75.