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Salvete ad paginam mathematicam!
  • Read about the number system in Latin in easy steps

  • Take an arithmetic quiz after each section (also on the Quizzes page)

  • On the other maths page you can read more about maths in the Roman World.

For Latin 'week' Head of Department Adam the Adder wants to talk about numbers in Latin. Each section deals with increasingly large cardinal numbers, and has a link to a quiz to test your knowledge.


The Latin number words derive from Proto Indo European (PIE). PIE is the ancestor of English, German, the Romance Languages, Russian, Iranian and Hindi as well as Latin and Greek. The Indo-European (IE) group of languages is the most commonly spoken, and most widely spread of all language groups. The number words have changed relatively little. 


unus ad decem






You’ll see the similarities. Why do we stop at ten? Because IE languages have decimal counting systems and that's because they counted with their fingers. Some tribes in the western US had base eight counting systems because they counted with the spaces between their fingers.

Anyhow, we’ve had base ten for millenia. If you think you could add numbers up to ten, try this quiz: Adding and subtracting up to decem in Latin. Like all the quizzes on this page they are of the ‘match the pairs’ type, so if you get stuck you should be able to work it out. 


decem ad viginti


Check out this list for numbers up to twenty:


  • eleven, undecim

  • twelve, duodecim

  • thirteen, tredecim

  • fourteen, quattuordecim

  • fifteen, quindecim

  • sixteen, sedecim

  • seventeen, septendecim

  • eighteen, duodeviginti

  • nineteen, undeviginti

  • twenty, viginti



Like English, the most common way of representing these numbers is by prefixing decem, or ten, with the number to be added to it. So thirteen = three and ten; tredecim = tres et decem. Simple. The exceptions In English are eleven and twelve which have lost their ‘ten’. There’s a difference again when we reach eighteen/duodeviginti, and nineteen/undeviginti. English keeps the additive principle (eight+ten), while Latin is subtractive (two from twenty). Which do you prefer? If you think you can remember these numbers, try this test: Adding & Subtracting up to Viginti


viginti ad centum


Now we need to represent multiples of ten of the numbers 2 to 9. That’s just eight numbers, and, just as five is a lot like fifty, the Latin numbers look a lot like the originals. I repeat viginti.


  • twenty, viginti

  • thirty, triginta

  • forty, quadraginta

  • fifty, qinquaginta

  • sixty, sexaginta

  • seventy, septuaginta

  • eighty, octoginta

  • ninety, nonaginta

  • hundred, centum



Viginti seems odd, but it actually comes from the same PIE root as duo. It ends in i, unlike all the others. septuaginta has an unexpected u and octoginta keeps the ‘o’ of octo. The ‘ginta’ or ‘ginti’ comes from the same PIE root as decem. It may seem like hundred and centum aren't cognate, but they are. If you think you have got the hang of these numbers, take this test: Adding and subtracting in tens up to Centum. Afterwards you can try: Adding and subtracting in ones up to Centum.


ducenti ad mille

No help given with English translations here, you'll have to work it out.


  • ducenti (duo centum)

  • trecenti (tres centum)

  • quadringenti (quattuor centum)

  • quingenti (quinque centum)

  • sescenti (sex centum)

  • septingenti (septem centum)

  • octingenti (octo centum)

  • nongenti (novem centum)

  • mille


This time Adam the Adder has not included any English, because Latin uses compound words as opposed to the two-word numbers of the English. These numbers decline, so i is the nominative plural of -centi, a plural only adjective. All the changes to the prefixes are for phonetic reasons; basically it's easier to say. To differentiate ducenti ad mille from viginti ad centum numbers try and remember the letters ent in centum and at the end of these numbers. Test yourself here: Multiples of centum up to mille. Mixing Latin multiples of ten (-inta) and 100 (-enti) can be confusing, so Dr Beaker's next quiz has multiples of 10 (above 100) at the beginning of the calculation, and multiples of 100 on the other: Multiples of decem up to mille.


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