Mechanical Counting and Calculating Devices

Mechanical counting and calculating devices have been used for centuries to aid in mathematical calculations. Over time, many different tools have been developed to help with various calculations. Here are ten of the most commonly used tools for mechanical counting and calculating: These include the following:


This is an ancient counting and mechanical calculating tool, meaning “counting frame” in Greek. It was initially a wooden frame with parallel grooves and coloured beads or sticks strung along it. When international trade became important, the abacus was used as a more advanced calculation device. Calculations were performed by moving the beads or sticks, adding for addition, subtracting for subtraction, and performing double addition or subtraction for multiplication and division. The abacus originated in China in 1200 and was widely used by clerks, traders, and merchants in Africa, Asia, and other parts of the world. The first line of beads counted units, the second line counted tens, the third line counted hundreds, and so on. It is still used in present times, and its users are referred to as abacists.

Mechanical Counting and Calculating Devices

Slide Rule

This device was invented in 1632 by William Oughtred, a British mathematician, who translated John Napier’s sticks into a slide rule. He called it the Napier bone, which was invented in 1617 and consisted of ten rods divided into nine squares and numbered from 0 to 9. Logarithmic tables came into use after the invention of logarithms. In 1654, Robert Bissaker presented a slide rule similar to those used today. Thomas Everard, a mechanic and tax inspector, greatly improved the construction of the slide rule by adding new features, such as “revolving scales”. Isaac Newton invented the “tongue”, which is an integral part of the slide rule. In 1950, Amedee Mannheim built a slide rule with a straight scale, which became the most widely used of all. The present-day slide rule consists of three parts: a frame, a “tongue” that can be moved along the grooves, and a “window” that can be shifted. The frame is divided into two halves to facilitate the movement of the “tongue”. There are seven scales on the front side of the slide rule – four on the frame and three on the “tongue”.

Mechanical Counting and Calculating Devices

The Stepped Reckoner

The Stepped Reckoner was a mechanical calculating machine designed by the German mathematician-philosopher Gottfried Wilhelm Leibniz in 1671 and built-in 1673. The machine was designed to perform multiplication and division and was named the Stepped Reckoner in reference to its purpose. The machine made use of wheels with teeth and was built during a time when Leibniz was a strong proponent of the binary system.

The binary system is ideal for use in machines because it requires only two digits, which can easily be represented by the on and off states of a switch. This made the binary system particularly suitable for use in electronic computers, as an electrical circuit can either be on or off, allowing for the representation of true and false values, and the flow of current directly representing the flow of logic.

Mechanical Counting and Calculating Devices

Calculating machine

A calculating machine is a mechanical device used for performing mathematical operations, such as addition, subtraction, multiplication, and division. It typically uses a series of gears, levers, and other mechanisms to perform the calculations.


The Comptometer is an electromechanical calculator that was first introduced in the 1880s. It features a keyboard with keys arranged in groups of five, allowing for rapid calculation of large numbers.

Adding machine

An adding machine is a mechanical calculator used for addition and subtraction. It typically has a series of numbered keys that can be pressed to add or subtract values.

Cash register

A cash register is a mechanical device used for registering and totalling sales transactions. It typically features a series of keys that correspond to different items or prices, as well as a drawer for holding cash.

Mechanical Counting and Calculating Devices


A planimeter is a measuring instrument used for finding the area of irregular shapes. It consists of a mechanical arm that traces the shape, and a series of gears and dials that calculate the area.

Curta calculator

The Curta calculator is a hand-held mechanical calculator used for performing complex calculations, such as square roots and trigonometric functions. It consists of a cylindrical body with a series of dials and knobs.

Mechanical Counting and Calculating Devices

Mechanical pencil

A mechanical pencil is a tool used for writing and drawing, featuring a replaceable lead that can be advanced using a mechanical mechanism. It is commonly used for drafting and technical drawing.


A micrometre is a precision measuring instrument used for measuring the thickness or diameter of objects with high accuracy. It consists of a calibrated screw and a set of jaws that can be adjusted to fit the object being measured.

Mechanical Counting and Calculating Devices

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