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∰

volume integral

Volume Integral

∰ marks integration throughout a closed three-dimensional region. In calculus and physics, it denotes a closed-volume integral; its circle signals closure, while ∭ alone does not.

Text symbol
Search it as
oiiint · closed volume · triple integral · closed integral · integral with a circle
Shows up in
Anything that takes text · its shape is whatever your font draws

What ∰ means

It means integrating throughout a closed three-dimensional region.

Its three strokes mark three-dimensional integration; the circle marks the closed boundary. A triple integral of density can give mass or charge; integrating 1 gives the region's volume.

Leibniz first used ∫ in a 1675 manuscript as a long S for Latin summa (“sum”); the shape represented adding tiny contributions.

Specialist notation for multivariable calculus and physics.

Do not use ∭ when the closed-boundary mark matters.

Don't confuse it with

2
∭
Triple Integral
Triple integral over three variables; the symbol alone does not mark the region as closed.
∯
Surface Integral
Closed surface integral, over the boundary rather than through the volume.

Questions people ask

1

Why does ∰ show as a box on some devices?

Because that device's fonts have no glyph for it. The character is still correct and still copies correctly — the box is a missing glyph, not a broken character.

How to type ∰

Windows (Word)
Alt+XType 2230, then Alt+X to get ∰.
Windows
Win+Rrun charmap for the full table, or use the emoji picker's Ω symbols tab (Win + .).
macOS
Control+Command+SpaceOpen the character viewer and search “volume integral”.
Linux
Ctrl+Shift+UType 2230, then Enter or Space.
HTML
∰
CSS
\2230
LaTeX
Use \oiiint if your LaTeX setup provides it; otherwise use a triple integral and state that the region is closed.
Codes and encoding1 code points
HTML decimal
∰
HTML hex
∰
CSS content
content: "\2230";
Each escape is closed by the next backslash; a trailing space is needed before a literal hex digit.
URL encoded
%E2%88%B0
1
On screen
1
Code points
1
JS .length
3
UTF-8 bytes

A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.

Families this belongs to

1

Maths & numbers1,835 symbols

1️⃣📏📐✖️➕➖➗🟰♾️#️⃣*️⃣0️⃣