free-symbols

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

UnicodeU+222D
HTML Entity∭
HTML Code∭
CSS\222D

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.