# How did the Romans perform mathematical calculations? **URL:** \ **Category:** Factual Questions\ **Created:** [February 14, 2015, 4:13am UTC](https://boards.straightdope.com/t/how-did-the-romans-perform-mathematical-calculations/712627 "2015-02-14T04:13:55Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![nschuhrke](https://avatars.discourse-cdn.com/v4/letter/n/ac91a4/32.png) [@nschuhrke](https://boards.straightdope.com/u/nschuhrke)\ **Post date:** [February 14, 2015, 4:13am UTC](https://boards.straightdope.com/t/how-did-the-romans-perform-mathematical-calculations/712627/1 "2015-02-14T04:13:55Z")
Obviously, Roman numerals are not suitable for performing mathematical computations, so what did they use. I read that the abacus was invested about 5,000 years ago and that its use quickly spread throughout the world. Did the Romans use an abacus to perform math computations? ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [February 14, 2015, 4:30am UTC](https://boards.straightdope.com/t/how-did-the-romans-perform-mathematical-calculations/712627/2 "2015-02-14T04:30:10Z")
[Roman Abacus](http://en.wikipedia.org/wiki/Roman_abacus)? ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [February 14, 2015, 4:40am UTC](https://boards.straightdope.com/t/how-did-the-romans-perform-mathematical-calculations/712627/3 "2015-02-14T04:40:25Z")
Roman numerals are not very convenient for doing arithmetic, but it can be done. It helps if you realize that the actual ancient Romans used a system somewhat simpler than the Roman numerals we are familiar with today. They did not use the prefix-subtraction feature, which was invented in the middle ages. For example, they would write VIIII instead of IX. That simplifies things a lot and lets you do some pseudo-positional manipulation. The algorithms for computing in Roman numerals this way were well known, but it was a real pain in the _culus_. ---
**Author:** ![johnpost](https://avatars.discourse-cdn.com/v4/letter/j/f17d59/32.png) [@johnpost](https://boards.straightdope.com/u/johnpost)\ **Post date:** [February 14, 2015, 4:48am UTC](https://boards.straightdope.com/t/how-did-the-romans-perform-mathematical-calculations/712627/4 "2015-02-14T04:48:13Z")
sharp chisels and soft stone. they also had piles of people refacing the stone. they reused the chips for road building throughout the empire. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [February 14, 2015, 7:44am UTC](https://boards.straightdope.com/t/how-did-the-romans-perform-mathematical-calculations/712627/5 "2015-02-14T07:44:31Z")
Just as there were professional scribes to do the reading and writing for businessmen who couldn’t do their own reading and writing, likewise there were professional arithmeticians (actually, scribes with additional years of special training) to do people’s arithmetic. They had big tables of arithmetic results (sums and products and such) that they used. I assume these were kept very closely guarded trade secrets. Today, most everybody in developed societies knows how to read, write, and do arithmetic. Yet we still hire specialized scribes to do the more advanced scribing, commonly called bookkeeping and accounting, and in the modern world just as in the ancient world we still hire specialized professionals to do our lawyering for us. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [February 14, 2015, 5:15pm UTC](https://boards.straightdope.com/t/how-did-the-romans-perform-mathematical-calculations/712627/6 "2015-02-14T17:15:10Z")
> [@Joey\_P](#): > > [Roman Abacus](http://en.wikipedia.org/wiki/Roman_abacus)? That’s a good reference; and I see that it mentions more than just the abacus: “For more extensive and complicated calculations, such as those involved in Roman land surveys, there was, in addition to the hand abacus, a true reckoning board with unattached counters or pebbles.” This makes me think that, in those days, _recording numbers_ and _calculating with numbers_ were seen as two separate things: you did your calculations using an abacus or counting board, and then you used Roman numerals to record your results. Sort of how a modern computer does its calculations by logically manipulating binary bits internally, and then displays its results by lighting up the appropriate pixels on the monitor in the pattern of Hindu-Arabic numerals. Roman numerals were in use in Europe until well into the Middle Ages. Fibonacci (of “Fibonacci sequence” fame) wrote his book [Liber Abaci](http://en.wikipedia.org/wiki/Liber_Abaci) to try to sell people on the “new” Hindu-Arabic way of writing and calculating with numbers. > [@](#): > > the intent of the book is to describe methods of doing calculations without aid of an abacus, and … for centuries after its publication the algorismists (followers of the style of calculation demonstrated in Liber Abaci) remained in conflict with the abacists (traditionalists who continued to use the abacus in conjunction with Roman numerals).