Pascalina: Description And Characteristics, Operation

The pascaline , also known as the arithmetic machine, is the first calculator to be produced, later becoming a device used by the public. It is rectangular with an interface based on rotating wheels. Pascalin gets its name from its inventor, Blaise Pascal.

Pascal was a French mathematician and philosopher, who managed to develop the artifact after three years of creation, between 1642 and 1645. As it was a fairly simple product, he was only capable of adding and subtracting figures; the user selected the figure in an interface. The Frenchman originally invented this product to help his father, a tax collector.

However, over the course of 10 years, Pascal produced 50 identical machines to distribute to various people in Europe. The pascaline is considered the first machine created to satisfy a commercial purpose, not counting the abacus created by the Greeks several centuries earlier.

Who invented it, when and how?

Pascalin was created by Blaise Pascal between 1642 and 1645. After its completion, the King of France assured Pascal that only he would be able to produce pascalins to sell through royal privilege.

However, the artifact was never commercially successful. This was because they were very expensive to develop independently, because the mechanisms were very difficult to create for the time (before the Industrial Revolution ).

For this reason, the owners of these objects usually placed them in their own homes and not in their offices. They were used as personal tools, which made them relatively unique.

Pascal created the object to assist his father in his calculations to count taxes. At that time a kind of abacus was used to count, which was impractical and the process was quite slow.

The abacus consisted of a series of stones that the user had to move from one side to the other in order to count effectively. Pascal’s tool, developed in France, was used to calculate in a mechanized way and much easier, reducing the margin of human error.


Pascal developed the machine with the help of some craftsmen from the city of Rouen, in France. In fact, according to the inventor’s sister, the biggest problem Pascal had was explaining to the Rouen artisans how the machine should be properly developed.

Although the craftsmen helped Pascal create more than one machine, they made the inventor lose his mind a bit, as they had a hard time understanding Pascal’s ideas.

Pascal developed this product when he was quite a young person; He was only 18 years old when he first created his mechanical calculator.

Description and characteristics

External part

A pascalina is a rectangular box that is approximately 12 inches long and 8 inches high. On the upper part of the machine there are 8 rotating discs that are divided according to the number of units with which each one works.

In each disc there are a total of two wheels, which serve to determine the number with which to work on each one. Above each disk is a number, which changes according to how each wheel is placed.

Each of the numbers is behind a small window (that is, an opening that allows you to see the number that is drawn on a piece of paper).

There is a small metal bar next to where the numbers are, which must be facing up if you want to use the machine to add.

Housing and materials

The piece responsible for keeping all the pascaline together, which is the box that contains all the mechanisms, was made of wood.

On the other hand, the internal materials that made up the mechanisms used to be made of iron pieces, which allowed the machine to function optimally.

How did it work?

Inner part

The inner part of a pascaline is the one that is made up of the entire counting system that allows the artifact to calculate additions and subtractions. That counting mechanism records the number of wheel spokes that each turn makes.

The most difficult part of the mechanism is that when one of the wheels makes a complete turn (that is, it adds all the numbers it allows), it must register the complete turn on the wheel next to it. In this way it is possible to add figures greater than 10 numbers.

This motion, which allows registering the complete return of one of the mechanisms to another adjoining mechanism, is called a transmission.

The higher the numbers you work with, the more difficult it is for the mechanism to work correctly.

For example, when working with several numbers that cause a figure greater than 10 000, the wheel that must register the “1” of the “10 000” must be able to register the change of the other 4 wheels that carry the “0” of the ” 10,000 “.

That record is usually quite complicated, because it puts a lot of pressure on the “1” wheel. However, Pascal designed a system capable of withstanding the pressure of change, allowing ascaline to work effectively.

Other mechanisms

Pascal used a special piece that was specifically used to carry out transport tasks between one wheel and another. It was a special lever that used the same gravity as a pushing force to transmit information from one piece to another.

In total there are 5 mechanisms and each one contains 2 wheels, which makes a total of 10 wheels. Each wheel has 10 small pins, which stick out of the paper to record the numbers.

Explaining everything in a simple way, the right wheel of each mechanism is considered as the units wheel, while the left is considered as the tens wheel. Every 10 spins of the right wheel represents one of the left wheel (that is, 10 units represent a ten).

All wheels turn counterclockwise. In addition, there is a mechanism that acts in the form of an arm, which stops the movement of the wheels when no type of addition or subtraction is being carried out.

With this mechanism, Pascal made that the wheels of the Pascalina could only be placed in fixed positions, which avoided an irregular movement of the pieces. Thus, the calculations were more precise and the machine’s margin of error was reduced.


Between each mechanism there is a lever, which is often referred to as the transmission lever. This lever helps the wheels register the rotation of all adjacent wheels.

This wheel consists of a series of different parts that allows its operation. In addition, it can rotate independently of the wheel to which it is attached. This movement is determined by the transmission pin, which is attached to the wheel.

The lever has some springs and small mechanisms that allow it to change position as the turning of the wheels determines its need.

The spring and a specialized piece to push the lever make it move depending on the direction in which each wheel turns.

Through this process, when the left wheel completes one turn, the right wheel moves once (to the next pin out of 10 total pins).

It is quite a complex mechanism. The design was particularly difficult to come by for the time, which made each piece quite complicated to build and the pascaline a very expensive object; In many cases, it was more expensive to buy a pascalina than to subsist a middle-class family for a whole year.

What was it for?

The machine process primarily made it possible to add and subtract two-digit numbers efficiently, without having to resort to manual calculation systems.

At that time it was very common to calculate figures through the use of writing or simply by using an abacus to carry out individual calculations.

However, these systems used to take a long time for people. For example, Pascal’s father would arrive home after midnight after spending much of his day counting numbers manually. Pascal developed this tool to speed up calculation tasks.

Although the tool worked as a means of addition and subtraction, it was also possible to divide and multiply using the pascaline. It was a slightly slower and more complex process for the machine, but it saved the user time.

To multiply or divide, the machine added or subtracted – respectively – several times the same code that was ordered. Repeated addition and subtraction allowed the owner of a pascaline to carry out more complex calculations using this machine.


In addition, the development of pascaline served as inspiration for future inventors to create new arithmetic calculation mechanisms.

In particular, pascaline is considered the main predecessor of more complex mechanisms, such as modern calculators and Leibniz wheels.


  1. Pascaline, MR Swaine & PA Freiberger in Encyclopaedia Britannica, 2017. Taken from
  2. The Pascaline of Blaise Pascal, Computer History Website, (nd). Taken from
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  5. Pascal’s Calculator, Wikipedia in English, 2018. Taken from
  6. The Pascaline And Other Early Calculators, A. Mpitziopoulos, 2016. Taken from

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