Therefore Symbol (∴) — How to Type, Copy & Paste

Copy the Symbol

Both forms of the symbol ready to copy:

∴ — Therefore (U+2234) — Copy this: ∴

Just highlight the symbol above and copy it to your clipboard. Paste it anywhere you need it.

What Does the Therefore Symbol Mean?

The therefore symbol (∴) is a mathematical and logical symbol that means "therefore" or "hence." It is placed before a conclusion that logically follows from the statements above it.

In formal logic and mathematical proofs, ∴ signals the result of a chain of reasoning. For example:

All humans are mortal. Socrates is human. ∴ Socrates is mortal.

The symbol has been used in mathematics since at least 1659, when Swiss mathematician Johann Rahn included it in his work Teusche Algebra. It is sometimes called the "therefore sign" or "ergo symbol."

The upside-down version (∵) means "because" and is its logical counterpart.

How to Type on Windows

There are several ways to type ∴ on Windows:

Alt Code: Hold down the Alt key and type 8756 on the numeric keypad. Release Alt and the symbol appears.

Character Map: Open Character Map (search "Character Map" in Start). Search for "therefore" and double-click it to copy.

Word/Office: Go to Insert > Symbol > More Symbols. Find ∴ in the mathematical operators section.

Emoji Panel: Press Win + Period (.) to open the emoji picker, then search for "therefore."

How to Type on Mac

On macOS, you have a few options:

Character Viewer: Press Cmd + Ctrl + Space to open the Character Viewer. Search for "therefore" and double-click to insert it.

Keyboard Shortcut: There is no direct keyboard shortcut for ∴ on Mac, but you can use the Character Viewer or set up a text replacement in System Settings > Keyboard > Text Replacements.

Hex Input: If you have Unicode Hex Input enabled, hold Option and type 2234.

How to Type on iPhone & Android

On mobile devices, the easiest method is to copy the symbol from this page.

iPhone: Copy ∴ from above. You can also add it as a text shortcut — go to Settings > General > Keyboard > Text Replacement and create a shortcut like "tfa" that expands to ∴.

Android: Copy ∴ from above. On some Android keyboards, you can find it under the symbols panel. Alternatively, use a clipboard manager to save it for quick access.

Uses of the Symbol

The therefore symbol appears in several fields:

Mathematics: Used in proofs to indicate a conclusion. Placed before the final statement that follows logically from previous steps.

Formal Logic: Marks the conclusion of a deductive argument. Works alongside the because symbol (∵) which marks premises.

Philosophy: Philosophical arguments sometimes use ∴ to mark logical conclusions, especially in formal logic courses.

Freemasonry: The therefore symbol has been used as a Masonic symbol, representing reason and logical deduction.

Typography: Occasionally used in decorative or academic typography to mark conclusions in published papers.

While less common in everyday writing, ∴ is essential in academic and professional settings where logical reasoning needs to be clearly marked.