Cardinal vs Ordinal Numbers: Definitions, Differences, Rules & Examples
In mathematics, grammar, and daily writing, numbers serve two fundamental but distinct purposes: measuring quantity (counting how many) and indicating sequence or position (ranking order). These two categories are known as cardinal numbers and ordinal numbers.
While they originate from the same numerical values, confusing the two—or misspelling their irregular written forms—is one of the most common errors in formal writing, legal documentation, and academic papers.
For fast conversion between numerals and words for any counting quantity, visit our Numbers To Word Converter or test reverse conversions using our Words to Numbers Converter.
Quick Comparison: Cardinal vs. Ordinal
| Feature | Cardinal Numbers | Ordinal Numbers |
|---|---|---|
| Core Question | “How many?” | “Which position or rank?” |
| Primary Purpose | Counting, measurement, quantity | Ordering, chronology, sequence, ranking |
| Examples (Digits) | 1, 2, 3, 4, 21, 100 | 1st, 2nd, 3rd, 4th, 21st, 100th |
| Examples (Words) | One, two, three, four, twenty-one | First, second, third, fourth, twenty-first |
| Fractions Relation | Forms the numerator (three fourths) | Forms the denominator (three fourths) |
| Common Uses | Ages, money, phone numbers, quantities | Competition rankings, dates, floors, centuries |
What Are Cardinal Numbers?
Cardinal numbers (also called counting numbers) express quantity. They tell us the magnitude or total size of a group without establishing any hierarchy or order.
- Examples:
- “There are seven continents on Earth.”
- “The invoice lists twenty-four individual items.”
- “She bought three books.”
Key Rules for Cardinal Numbers:
- Zero is a cardinal number: It signifies an empty quantity or null set.
- Cardinal numbers cannot have ordinal suffixes: Writing “I have 2nd pencils” is grammatically incorrect.
- Hyphenation: Compound cardinal numbers between 21 and 99 must always be hyphenated (e.g., thirty-five, seventy-two).
What Are Ordinal Numbers?
Ordinal numbers specify sequence, order, priority, or rank within an ordered set. Rather than counting how many items exist, they tell us where a particular item sits relative to others.
- Examples:
- “She finished in first place.”
- “Our office is on the twelfth floor.”
- “This marks the twenty-first century.”
Suffix Rules for Written Ordinals
In abbreviated numeric form, ordinal numbers combine the base numeral with a two-letter suffix corresponding to the last word of the spelled-out number:
- -st is added to numbers ending in the sound one (1st, 21st, 31st, 101st). Exception: 11th (eleventh).
- -nd is added to numbers ending in the sound two (2nd, 22nd, 32nd, 102nd). Exception: 12th (twelfth).
- -rd is added to numbers ending in the sound three (3rd, 23rd, 33rd, 103rd). Exception: 13th (thirteenth).
- -th is added to almost all other numbers (4th, 5th, 6th, 11th, 12th, 13th, 20th, 100th).
Irregular Spelling Changes in Ordinal Numbers
When converting cardinal words to ordinal words, several spelling adjustments occur:
1. The “ve” to “f” Transformation
- Five (5) becomes Fifth (5th) — NOT “fiveth”.
- Twelve (12) becomes Twelfth (12th) — NOT “twelveth”.
2. Dropping or Adding Letters
- Eight (8) becomes Eighth (8th) — Add only an h, not th (NOT “eightth”).
- Nine (9) becomes Ninth (9th) — Drop the silent e (NOT “nineth”).
3. Words Ending in “y” (Tens)
For tens like twenty, thirty, forty, change the final -y to -ie- before adding -th:
- Twenty $\rightarrow$ Twentieth
- Thirty $\rightarrow$ Thirtieth
- Forty $\rightarrow$ Fortieth
- Fifty $\rightarrow$ Fiftieth
- Ninety $\rightarrow$ Ninetieth
4. Compound Ordinals
In compound numbers, only the final word takes the ordinal form; the preceding tens words remain cardinal:
- 21st: Twenty-first (NOT “twentieth-first”)
- 53rd: Fifty-third (NOT “fiftieth-third”)
- 194th: One hundred ninety-fourth
Master Reference Table: 1 to 31 (Calendar Range)
This table covers the most critical numbers used in dates, rankings, and day-to-day writing:
| Numeral | Cardinal Word | Ordinal Word | Ordinal Abbreviation |
|---|---|---|---|
| 1 | One | First | 1st |
| 2 | Two | Second | 2nd |
| 3 | Three | Third | 3rd |
| 4 | Four | Fourth | 4th |
| 5 | Five | Fifth | 5th |
| 6 | Six | Sixth | 6th |
| 7 | Seven | Seventh | 7th |
| 8 | Eight | Eighth | 8th |
| 9 | Nine | Ninth | 9th |
| 10 | Ten | Tenth | 10th |
| 11 | Eleven | Eleventh | 11th |
| 12 | Twelve | Twelfth | 12th |
| 13 | Thirteen | Thirteenth | 13th |
| 14 | Fourteen | Fourteenth | 14th |
| 15 | Fifteen | Fifteenth | 15th |
| 16 | Sixteen | Sixteenth | 16th |
| 17 | Seventeen | Seventeenth | 17th |
| 18 | Eighteen | Eighteenth | 18th |
| 19 | Nineteen | Nineteenth | 19th |
| 20 | Twenty | Twentieth | 20th |
| 21 | Twenty-one | Twenty-first | 21st |
| 22 | Twenty-two | Twenty-second | 22nd |
| 23 | Twenty-three | Twenty-third | 23rd |
| 24 | Twenty-four | Twenty-fourth | 24th |
| 25 | Twenty-five | Twenty-fifth | 25th |
| 26 | Twenty-six | Twenty-sixth | 26th |
| 27 | Twenty-seven | Twenty-seventh | 27th |
| 28 | Twenty-eight | Twenty-eighth | 28th |
| 29 | Twenty-nine | Twenty-ninth | 29th |
| 30 | Thirty | Thirtieth | 30th |
| 31 | Thirty-one | Thirty-first | 31st |
How to Write Dates: Cardinal vs Ordinal
Date formatting creates frequent confusion between written text and spoken English:
- When the day follows the month: Standard style manuals (Chicago, AP, MLA) require cardinal numerals in written text, even though speakers pronounce them as ordinals:
- Written: July 4, 1776 (or July 4th only in informal correspondence).
- Spoken: “July fourth, seventeen seventy-six.”
- When the day precedes the month: Both formats occur, but formal documents spell out the ordinal:
- “The fourth of July”
- “The twenty-first of September”
Nominal Numbers: The Third Category
Beyond cardinal (quantity) and ordinal (order), linguists identify a third group: nominal numbers. A nominal number serves solely as a label, code, or identifier. It has no quantitative value and does not indicate rank:
- Zip codes (e.g., 90210)
- Jersey numbers (e.g., Michael Jordan’s #23)
- Telephone numbers (e.g., 555-0199)
- Flight numbers (e.g., Flight 815)
Frequently Asked Questions (FAQ)
Is zero a cardinal or an ordinal number?
Zero is strictly a cardinal number. It represents the count of nothing (n = 0). In standard ranking systems, there is no “zeroth” place in human competitions or calendar dates, although computer science frequently uses zero-based indexing where index 0 represents the first element.
Why is 11th “eleventh” and not “eleventh-first”?
In Germanic linguistics and Old English, numbers 11 and 12 developed independent etymological roots (endleofan meaning “one left over” and twelif meaning “two left over”). As a result, 11, 12, and 13 do not end in -st, -nd, or -rd; they take the standard -th suffix (11th, 12th, 13th).
What is the correct spelling: “twelveth” or “twelfth”?
The correct spelling is always twelfth. The “ve” in twelve softens to an “f” before the “th” is added. Writing “twelveth” is a misspelling.
Should ordinal suffixes be written as superscripts (1st or 1st)?
Modern typographical guidelines (including AP Style and Chicago Manual of Style) recommend using plain text (1st, 2nd, 3rd) rather than superscript (1st, 2nd, 3rd). Superscripts can disrupt line spacing (leading) in printed books and web typography.
How do ordinals work with centuries and decades?
Centuries are always expressed with ordinals: the twenty-first century (21st century). Decades, however, are cardinal: the 1990s (nineteen nineties).