Triple Integral Symbol
∭ is the triple integral symbol used to represent integration over three-dimensional space.
U+222D
The symbol ∭ is read as a triple integral. It’s commonly used in mathematics, physics, and engineering to denote integration over a volume in 3D. Use it in notes, documents, and code when writing calculus expressions.
Triple Integral Symbol Meaning
∭ (TRIPLE INTEGRAL, U+222D) denotes a triple integral, which means integrating a function over a three-dimensional region (a volume). In practice, it extends the idea of single and double integrals to three dimensions, often written with variables like x, y, and z and bounds for each. Triple integrals are used to compute quantities such as total mass from a density function, volume with integrands that depend on space, and energy or flux-related expressions in physics. When using text or code, the symbol can be inserted directly or via its character encodings like HTML entity (∭) and Unicode escapes.
Common uses
- •Writing calculus expressions for integrals over a 3D volume in homework or study notes
- •Formulating physics problems such as total mass from density ρ(x, y, z)
- •Computing volume or average values using an integrand over x-y-z bounds
- •Specifying multi-variable integration steps in engineering and technical documentation
- •Labeling expressions in reports, math slides, and formulas in design tools
Examples
∭ Triple Integral Symbol: Copy & Use
- ∭Compute ∭_V ρ(x,y,z) dV.
- ∭The volume is given by ∭_V 1 dV.
- ∭Evaluate ∬_R (∫ f d x) dA using a triple integral form ∭ f dV.
- ∭Find the total charge Q = ∭_V ρ dV.
- ∭Set up ∭_D g(x,y,z) dx dy dz for the region D.
Variations
Ready to copy
Technical codes
| Unicode | U+222D | |
| HTML Entity | ∭ | |
| HTML Code | ∭ | |
| CSS | \222D | |
| Alt Code | Alt + 8749 | |
| Decimal | 8749 |
How to type Triple Integral Symbol (∭)
On Windows
Hold Alt and type 8749 on the numeric keypad. In Word, type 222D then press Alt + X.
On Mac
Switch to the Unicode Hex Input keyboard, then hold Option and type 222D. Or press Control + Command + Space and search.
On Linux
Press Control + Shift + U, type 222d, then press Enter or Space.
Anywhere
Copy ∭ with the button above and paste it wherever you need it — this works on every device and in every app, with no keyboard shortcut to remember.
FAQ
What does the Triple Integral symbol mean?
∭ (TRIPLE INTEGRAL, U+222D) denotes a triple integral, which means integrating a function over a three-dimensional region (a volume). In practice, it extends the idea of single and double integrals to three dimensions, often written with variables like x, y, and z and bounds for each. Triple integrals are used to compute quantities such as total mass from a density function, volume with integrands that depend on space, and energy or flux-related expressions in physics. When using text or code, the symbol can be inserted directly or via its character encodings like HTML entity (∭) and Unicode escapes.
How do I type or copy the triple integral symbol (∭)?
Copy the character “∭” directly from this page, or use the provided encodings: HTML entity ∭ or Unicode escapes like \\u{222D}.
What is the difference between a triple integral and a double integral?
A double integral integrates over a 2D region (often using two variables), while a triple integral integrates over a 3D region or volume (typically using x, y, z).
What do the bounds usually look like with ∭?
Triple integrals are commonly written with limits for each variable, such as ∭_D f(x,y,z) dx dy dz, where D defines the 3D region.
What is the Unicode information for ∭?
The symbol is TRIPLE INTEGRAL with Unicode code point U+222D. It can be referenced as HTML entity ∭ and CSS escape \\222D.