What mathematical machine did Leonardo da Vinci design to perform arithmetic calculations?

Leonardo da Vinci designed a mechanical calculator using geared wheels to perform arithmetic operations.

A drawing in the Codex Madrid shows a calculator-like mechanism with numbered wheels and linked gears. Turning one wheel could transmit motion to another, creating a system for representing and manipulating numerical values. The design is usually interpreted as an early calculating machine, although its exact intended operation remains debated.

Leonardo’s machine was not an electronic calculator and was not documented as a completed working instrument. Historians therefore distinguish between the surviving drawing and claims that Leonardo built a functioning calculator. The mechanism nevertheless demonstrates his understanding of carrying motion between decimal positions, a key problem in mechanical arithmetic.

Later inventors developed practical calculating machines, including Blaise Pascal’s Pascaline in the seventeenth century. Leonardo’s design predates those machines by more than a century, but it should be described cautiously as a mechanical calculator concept rather than as the first proven working calculator.