What is a triple integral?
An integral of a function of three variables over a solid region.
Triple Integral Calculator
Integrate a constant density over an axis-aligned box to get k times the box volume.
Enter the box and density
Provide constant k and the three pairs of bounds.
About this calculator
How to use Triple Integral Calculator, plus the formulas and logic behind the results.
Tool description
For a constant integrand, the triple integral equals k times the volume of the rectangular box.
How to use
- Enter the constant density k.
- Enter x, y, and z bounds of the box.
- Select Calculate to view ∭ k dV.
- Set k = 1 to recover the geometric volume.
Formulas & reference
∭_B k dV = k (b−a)(d−c)(f−e)
Triple integral tips
- k = 1 → volume of the box
- Mass of uniform density ρ is ρ·volume
- Order of dx dy dz does not matter for constants
- Negative edge lengths flip the oriented volume sign
Calculation logic
Multiplies the three edge lengths by the constant integrand.
Educational box case only—no spherical or cylindrical coordinates.
Triple Integral Calculator FAQ
Common questions about this calculator and how to use the results.
Why only constants?
They give a clear first example: density × volume.
What if k = 1?
You get the volume of the rectangular box.
Are curved solids supported?
Not in this tool.
Can bounds be negative?
Yes—use any real endpoints.
Is this free?
Yes.