Latin Numerals: Counting with Ordinals & Cardinals

Have you ever heard someone speak about the primary, secondary, and tertiary of something—only to wonder what they would have called the next element? Well, this crash course on Latin numerals will help clear things up!
latin numerals ordinals cardinals alpharithms

Ever wonder what comes after primary, secondary, or tertiary in counting sequences? These terms come from Latin numerals which are expressed in Cardinal, Ordinal, and several other forms. These terms are used to describe the rank order in which an element exists relative to other elements.

For example—the Latin Ordinal primus, meaning first, gives us primary is used to describe the first-order rank of an element. Primary elections, primary contact, primary residence—these all indicate the first of something where there may be others.

Naming the Numerals

These terms are used in variation throughout the fields of Science, Engineering, and Mathematics as ways to count and signify order as well as sometimes to simply assign arbitrary taxonomic value. Below is a collection of the first 10 Latin numerals though they continue far beyond.


Ordinal: Primus

Cardinal: Unus

The first element of a counting sequence and also used to indicate the principle matter of importance. Examples include primary elections, primary schools, and primary contact numbers. The word Primary finds its root from the Latin words primus and arius used to indicate a primary rank in military contexts or, similar to its modern use, the principal matter of concern.


Ordinal: Secundus

Cardinal: Duo

Secondary describes the term directly preceding the primary term or element in a counting sequence or the primary matter of concern. Examples of secondary include secondary elections, secondary schools, or a secondary coil in certain electrical circuits. The word secondary comes from the Middle English secundarie which is descended from the Latin word secundus that means “to follow” and can be compared with the term sequor which bears the same meaning.


Ordinal: Tertius 

Cardinal: Tres

Tertiary is used to describe the third level within a sequence of elements, events, or otherwise meaningful distinctions. Example In Geology, Tertiary refers to the first period of the Cenezoic era. Tertiary comes from the Latin word tertius which means third. Examples include tertiary compounds in chemistry describing those that have been subjected to the substitution of 3 atoms.


Ordinal: Quartus

Cardinal: Quattuor

Quaternary is used to describe an element as being of fourth-order rank in a sequence or collection. In Geology, the term quaternary is used to describe the most recent period in the Cenozoic era, directly proceeding the Tertiary Period. Quaternary comes from the Latin quarternarius meaning “to contain or be made of four,” which is a combination of the words quaterni and arius. In chemistry, the term quaternary describes certain types of compounds including amines and ammonium salts.


Ordinal: Qunitas

Cardinal: Quinque

Quinary is used to describe an element of fifth-order rank or, more generally, to describe something made of five sub-units. The term quinary comes from the Latin word quinarius meaning “containing five each” which represents a combination of the terms quinus and arius. In Zoology, quinary refers to an outdated system of classification by which the Animal kingdom was divided into 5 subkingdoms and each subkingdom was divided into five subclasses. Quinary also refers to a numeral system that uses 5 as the base value—possibly having come about in connection to there being five fingers on the human hand.


Ordinal: Sextus

Cardinal: Sex

Senary is used to describe an element of six-order rank within a larger sequence or collection. It comes from the Latin term senarius meaning “consisting of six each” which is a combination of the words seni and arius. In mathematics, a senary numeral system is also known as a base-6 or heximal number system. It is thought the senary numeral systems evolved from the use of five fingers and the closed fist to represent terms 0-5 (six total terms.)


Ordinal: Septimus

Cardinal: Septum

Septenary is used to describe an element of seventh-order rank within a sequence or collection of elements. It comes from the Latin term septenarius meaning “consisting of seven each” and is made of the terms septeni and arius. Septenary is used in Theosophy to describe the seven principles of man, and also describes the system of counting 7-day weeks in some contexts.


Ordinal: Octavus

Cardinal: Octo

Octonary is used to describe an element of seventh-order rank within a sequence or collection of elements. It comes from the Latin term octonarius meaning “containing eight” which is made of the terms octoni and arius. Octonary can be used to refer to the style of poetry using 8-lines. While similar in concept, Octonary is not used to describe octal counting systems—a means of numerical representation in computer science.


Ordinal: Nonus

Cardinal: Novem

Nonary is used to describe an element of ninth-order rank within a collection or sequence of elements. It comes from the Latin term nonarius meaning “containing nine” which is a combination of the terms nonus and arius. Nonary is used to describe less common base 9 counting systems where the digits 10 represent the value 9. In decimals, a nonary counting system uses only digits 0-8 similar in concept to how binary systems use the values 0-1.


Ordinal: Decimus

Cardinal: Decem

Denary is used to describe an element of tenth-order rank within a system, collection, or sequence of elements. It comes from the Middle English term denarie which evolved from the Latin term denarius meaning “containing ten” which was sometimes used as denarius nummus to describe a coin of ten subunits. Denary is often used to describe the decimal counting system which uses a base of 10.

Beyond Ten

The numeral system presented here is the Latin version (latinate) of the English Ordinal Counting system. There are a great many more in this sequence but, other than a few terms such as hexadecimal, the terms become increasingly rare in their usage. For a full listing of these terms just check out the Wikipedia entry for numerical systems which includes a more exhaustive listing—albeit with a sparser presentation of definition.

Zαck West
Full-Stack Software Engineer with 10+ years of experience. Expertise in developing distributed systems, implementing object-oriented models with a focus on semantic clarity, driving development with TDD, enhancing interfaces through thoughtful visual design, and developing deep learning agents.