# The Medieval Calculator

Detail from The Calling of Saint Matthew by Caravaggio (1599) showing Matthew counting coins at a counting table.

### How Our Ancestors Managed Their Money

The electronic calculator today has become so ubiquitous that we can pick one up at nearly any local grocery store for less than \$5. My children have grown up in a generation that can hardly imagine life without a computer or smart phone. I, on the other hand, can remember the tiny general store in my hometown of Belfry, Kentucky with its bulky mechanical adding machine. It had number keys similar to a manual typewriter arranged in rows that represented various denominations. If you wanted to enter the amount \$12.47, for example, you would simply depress the number one in the column that represented tens, the number two in the column that represented ones, and the numbers four and seven in the two columns that represented decimal places. As I recall, the highest denomination represented was hundreds. Once the proper keys were depressed, you would pull a lever on the side of the machine and the number would be added to a running total.

Have you ever wondered what people did before such mechanical innovations? If you write historical fiction set prior to the Georgian period, you may want to think about it. Most people assume that they simply performed their calculations in longhand like we were taught in school. This is probably true from about the mid-seventeenth to early eighteenth century onward. But one must remember that, during the medieval period and perhaps another century and a half or so afterwards, European society still held firmly to the Roman numerical system of I, V, X, L, C, D, and M. This system was fine for recording a number in written form, but was extremely cumbersome for even simple calculations. It would be well into the sixteenth century before the Hindu-Arabic numbering system that we use today, with its concept of decimal places and the introduction of zero, came into general use. Even then, people were reluctant to embrace such a radical change and figures arrived at using the “new math” were often verified by utilizing the old method. It took several generations before the new system was universal across Europe. An example of the transition between the two systems can be found in the document below.

The rent rolls from Bristol, England. The figures on the left side, recorded in 1599, are a form of stylized Roman numerals. Those on the right, recorded in 1640, are Hindu-Arabic. From http://ds.haverford.edu/bitbybit/bit-by-bit-contents/chapter-one/from-the-abacus-to-hindu-arabic-numerals/

Before that, computations beyond those that could be easily worked out in a person’s head were done on a counting board or reckoning table. A counting board is simply a flat surface inscribed with horizontal lines representing various denominations. It functions similar to what we would recognize as an abacus today.

Rare surviving medieval counting table now in the Musee de l’Oeuvre Notre Dame in Strasbourg.

Counting table – detail. The lines and symbols are inlaid ivory.

In the early medieval period, before the Norman conquest of England, the counting board was as simple as a flat sand surface with inscribed lines using small stones or pebbles as counters. In fact, our word calculate comes from the Latin word calculus meaning small stone. By the high Middle Ages, however, the process had evolved into a wooden table with lines painted or carved on the surface and using mass-produced metal tokens called jettons (pronounced ‘jet-ensfor counters. To the untrained eye, jettons look nearly identical to old coins and many a metal detectorist has been disappointed to find that his newly discovered ancient silver coin is simply a copper-alloy jetton of little value. Think of a token used in a 1980s video parlor.

Any wealthy merchant, lord, or administrator would have had a counting table. If it was located in a purpose-built room, it would be known as the counting house. Do you remember the lines from the old nursery rhyme Sing a Song of Six Pence that went “The king was in his counting house, counting out his money. The queen was in the parlor eating bread and honey”? Well now you know how he was doing it.

Counting table from an early woodcut

Very few examples of counting tables still survive, presumably because, as a table, they were simply repurposed and remained in use until they were discarded. We do, however, have a number of illustrations from the time that show them in use. Their operation is reasonably simple. Jettons would be placed upon the right hand side of the board to represent a starting number. The value of each jetton was determined by its location on the board. There were consecutive horizontal lines which represented various denominations, similar to the columns of keys on our adding machine example at the beginning of this post. Starting from the bottom, the lines represented ones, tens, hundreds, thousands, and so on. The space between two consecutive lines denoted five units of the denomination located on the lower of the two lines. For example, to represent the number fifteen, a jetton would be placed on the ten line and another in the space between the ten and one.

Another early woodcut depicting a counting table in use

A vertical line, or sometimes multiple lines, would divide the board into sections. Addition would be carried out on the right hand side of the board and subtraction on the left. Let’s assume you wanted to add ten to your starting number of fifteen. You would simply place another jetton on the right hand side of the board on the ten line. You now have two jettons on the ten line and one jetton between the ten and one. Your answer then is twenty five. If you were subtracting ten, rather than adding, the jetton would be placed on the ten line on the left hand side of the board. You now have two jettons on the ten – one on either side of the vertical line – thereby cancelling one another out. Removing both jettons from the ten leaves you with a single jetton between the ten and one, or five.

Multiplication and division could also be carried out on a counting board but was considerably more complicated. Video clips describing these operations can be found here and here.

We have many surviving examples of medieval jettons from all over Europe and the huge variety of designs demonstrates just how widely they were in use. It was not at all unusual for a king or powerful lord to have jettons cast with their own image or coat of arms. They would be used not only in their own households, but would have presumably been given as gifts to visitors or dependents. Although most were made of copper or bronze, we do have examples of silver and gold that were minted for very high-status individuals. Some examples have been intentionally pierced, we think, to prevent them from being gilded and passed off as coins, which did happen.

English jetton from the time of Edward III

French jetton

We still see traces of this interesting method of calculation in our world today. We have already mentioned the use of the abacus, which can still be found in some Asian societies. Tokens, or jettons, are also still fairly common, although their use has evolved. They are used most frequently as advertising or as a surrogate for money for a specific purpose, such as poker chips or for use in a vending machine or video game. But most of us have probably failed to make the connection with the one modern example with which we are likely most familiar. The chief finance minister in the United Kingdom is referred to as the Chancellor of the Exchequer. The name derives from the counting table used by the crown treasurer in medieval England. It is described in a fascinating document now held by Yale University called Dialogue Concerning the Exchequer, written by Richard FitzNeal in 1190. It states:

“The exchequer is a quadrangular surface about ten feet in length, five in breadth, placed before those who sit around it in the manner of a table, and all around it it has an edge about the height of one’s four fingers, lest anything placed upon it should fall off. There is placed over the top of the exchequer, moreover, a cloth bought at the Easter term, not an ordinary one but a black one marked with stripes, the stripes being distant from each other the space of a foot or the breadth of a hand. In the spaces moreover are counters placed according to their values…Although, moreover, such a surface is called exchequer, nevertheless…the court itself which sits when the exchequer does is called exchequer; so that if at any time through a decree anything is established by common counsel, it is said to have been done at the exchequer of this or that year.”

So even though it would appear that we have come a long way technologically, we are still very much connected to those who have gone before us in more ways than we recognize or care to acknowledge. I am reminded of the wise counsel of my dear parents. “Never forget where you came from.” I think they were right.

## 12 thoughts on “The Medieval Calculator”

1. bookheathen says:

Congratulations on a fine piece of research, James!

• Thank you, Andrew. I am grateful that there are people out there who are interested in the same obscure facts that hold such a fascination for me. Cheers.
Jim

2. A really thorough post, James, with a wealth of interesting detail. I do like your final paragraph, in which you put all the great advances we enjoy today into persective.

• Thank you, Millie. I appreciate you stopping by and taking the time to comment.
Jim

3. Fascinating. I’ve read some fictional books set in the area but never got much detail on the counting methods…They make perfect sense. Thanks James!

• Thanks for the comment, Olga. I am glad you found it interesting.
Jim

4. Lisa says:

Thank you, this is very through but concise. i will be referencing your page in a project I’m working on,

• You are very welcome,Lisa. I am glad you found it useful.
Jim

5. Fascinating post – didn’t realize the origins of the Chancellor of the Exchequer. Like many other readers, some things till I read them I don’t realize that I enjoy them and how fascinating the topic itself is. Thanks for writing this.