Early people calculated using their bodies, simple marks, and gradually more sophisticated counting tools long before written numbers or electronic calculators existed.

Body-based counting

The very first ā€œcalculatorsā€ were human bodies.

  • Fingers and toes were used to count animals, people, or traded goods, often forming the basis of baseā€‘10 counting systems.
  • Some cultures also used the 12 finger joints (excluding the thumb) as a way to count up to 12 on one hand, combining this with the other hand to reach up to 60, which helped inspire baseā€‘60 systems like those in ancient Mesopotamia.
  • Simple spoken number words or chants went along with pointing at each item, turning counting into a repeated, almost rhythmic process.

A quick example: a herder might tap each sheep on a gate with one hand while raising fingers on the other hand to keep track of tens.

Tally marks and counting bones

Once groups grew larger, people needed memory aids beyond fingers.

  • Early humans carved notches in bones or sticks to track counts, like days, animals, or trade items.
  • Famous artifacts like the Lebombo bone show rows of incisions that likely worked as talliesā€”essentially a portable counting notebook.
  • Each notch represented ā€œone,ā€ and people could group notches (for example in fives) to make reading larger numbers easier.

This is basically the ancestor of the tally marks you might still use today (four vertical lines with a diagonal fifth).

Pebbles, knots, and simple devices

As societies became more organized, tools for calculation became more varied.

  • Pebbles or small stones were used as counters; the Latin word calculus (small stone) is where our word ā€œcalculatorā€ comes from.
  • People used knotted strings to record counts and simple calculations; in later cultures like the Inca, complex knotted cords called quipu stored numerical information for taxes and census-like records.
  • Grains, seeds, and shells were also common counters, especially in farming societies where people needed to track harvests and debts.

To add, they might put more pebbles into a pile; to subtract, they removed some. Multiplying could be done by repeatedly adding piles.

Counting boards and early abacus-style tools

Over time, flat surfaces specifically designed for calculation appeared.

  • Ancient Greeks, Babylonians, and Romans drew or carved parallel lines on tables or boards and placed pebbles on them; these counting boards were used to add and subtract.
  • Each line represented a place value (like units, tens, hundreds), and the position of pebbles on those lines determined the number, similar to a place-value system.
  • In the Americas, cultures like the Mayans or Incas used grains or stones on similar ideasā€”lines or sections where the placement of counters encoded values.

Adding meant putting extra counters on their lines; when enough accumulated (for example five or ten), they would remove them and move a counter to the next line up, just like ā€œcarryingā€ in modern addition.

Early written numbers and advanced calculations

Once writing developed, calculation and recordā€‘keeping became more powerful.

  • The ancient Sumerians in Mesopotamia created written numbers on clay tablets for tradeā€”grain, workersā€™ wages, silver, and other goodsā€”around 3000 BCE.
  • They used a baseā€‘60 (sexagesimal) system for many calculations; this is why we still have 60 minutes in an hour and 360 degrees in a circle today.
  • Clay tokens and sealed clay balls (bullae) were used as physical accounting tools; later, impressions of those tokens evolved into written number symbols on tablets.

Even at this stage, people still often used physical counters, fingers, or boards for doing the actual math, and then wrote the final results in their number systems.

Mini wrapā€‘up (TL;DR)

  • Bodies first : Fingers, toe-counting, and finger joints for simple counting.
  • Marks and bones : Notched bones and tally sticks to remember how many.
  • Counters : Pebbles, grains, knots in strings to track and manipulate quantities.
  • Boards and abaci : Counting boards with lines and counters as early ā€œmachinesā€ for addition and subtraction.
  • Written numbers : Sumerian, Babylonian, and other early systems turned these practices into structured mathematics and recordā€‘keeping.

Information gathered from public forums or data available on the internet and portrayed here.