QED stands for quod erat demonstrandum, a Latin phrase meaning "which was to be demonstrated" or, in looser English, "which is what we set out to prove." Mathematicians write it at the very end of a proof to signal that the claim made at the start has now been shown to be true.
You will meet it most often in a high school geometry class, a college proof course or a logic textbook. Outside the classroom, people sometimes say it with a grin after winning an argument, as if to say "and there you have it."
Quick facts
Stands for
Quod erat demonstrandum (Latin)Plain meaning
What we wanted to prove has been provedType
Initialism, said as three lettersWritten as
QED, Q.E.D. or a small black squareUsed in
Geometry proofs, logic, philosophy, debateOther meaning
Quantum electrodynamics in physics
QED stands for three Latin words
The phrase has three Latin words, and each one maps to a letter.
| Letter | Latin | Rough English |
|---|---|---|
| Q | Quod | Which, that |
| E | Erat | Was |
| D | Demonstrandum | To be shown, to be proved |
So a word for word reading is "which was to be shown." The idea is that the proof opened with a goal, and the last line confirms the goal has been reached. Because you say each letter, "Q E D," it counts as an initialism. Acronym vs abbreviation covers that label in more depth.
How QED closes a geometry proof
In a two column proof, students list statements on the left and reasons on the right. After the final statement matches what the problem asked you to prove, a teacher may want you to mark the finish.
From a homework sheet: "Given: AB = CD. Prove: AC = BD." After four steps, the last line reads "AC = BD, segment addition." A student writes QED below it. The letters tell the grader the argument is complete and nothing is missing.
Geometry proofs about triangles often use CPCTC as one of the last reasons, right before the QED. In college courses, many professors expect the same signal, though some prefer a symbol instead of letters.
Ways to write it: letters, periods and the box
- QED, all capitals and no dots, is the most common modern form.
- Q.E.D. with periods is older and still correct, especially in formal print.
- ∎ or □ is a small filled or open square that many textbooks and journals use in place of the letters. People call it the end of proof mark or the tombstone.
- QEF, quod erat faciendum, "which was to be done," shows up in old texts after a construction rather than a proof. It is rare today.
Whichever you choose, use it on every proof in the assignment. Lowercase "qed" looks like a typo in formal work.
Where the phrase came from
Ancient Greek mathematicians, including Euclid, ended proofs with a Greek phrase that carried the same meaning. Later scholars who wrote in Latin translated that ending as quod erat demonstrandum, and the Latin version spread through European math books. Over time, writers cut it down to the three initials, and English speakers kept them.
That history explains why a modern American classroom still uses a Latin tag. Like i.e. and AD, it is a piece of old Latin that survived inside a short form.
QED in conversation and other fields
Outside math class, people use QED as a playful mic drop at the end of a point. "You said the store closes at nine. It is 9:05 and the doors are locked. QED." The tone is light and a little smug, so save it for friends rather than a tense meeting.
| Field | QED means | Example |
|---|---|---|
| Math, logic | Quod erat demonstrandum | The last line of a proof |
| Physics | Quantum electrodynamics | The theory of how light and charged particles interact |
| Everyday talk | "I rest my case" | Ending a friendly debate |
Context almost always settles it. A physics lecture on photons points to quantum electrodynamics; a proof sheet points to the Latin.
Quick tips for students
- Only write QED when the last statement truly matches the "Prove" line.
- Do not use it after a single calculation; it belongs to arguments.
- If your teacher uses the square symbol, copy that habit.
- Say it as three letters, "cue ee dee," not as a word.
The school acronyms section collects other letters from handouts and report cards, and STEM covers the broad field where QED belongs.
Questions people ask
What does QED stand for in math?
In math, the letters abbreviate the Latin phrase quod erat demonstrandum. It translates as "what had to be shown," and it goes at the end of a proof to show the required statement has been proved.
Do you have to write QED at the end of a proof?
No. It is a custom, not a rule. Some teachers ask for it, others accept a small square, and many published proofs simply end with a clear final sentence.
How do you pronounce QED?
Say the three letters: "cue ee dee." Nobody reads the full Latin aloud in class, though you can if you want to sound formal.
Is QED the same as "I rest my case"?
In casual speech it plays a similar role, wrapping up an argument with confidence. In math it is more precise, because it marks the point where a stated goal has been logically reached.
Should QED have periods?
Both QED and Q.E.D. are correct. Modern math writing usually drops the periods, while older books and some style guides keep them.