Triangular Prism Volume Calculator
Triangular prism volume calculator with multiple methods: base & height, three sides (Heron’s formula), or base area and length. Returns volume in cubic units, m³, liters and more, with step-by-step formulas.
Full original guide (expanded)
Triangular Prism Volume Calculator
Base area × length with Heron supportCompute triangular prism volume from base/height, three sides (Heron’s formula), or base area and length.
Returns volume in multiple units and shows the formulas used.
1. Enter triangular prism dimensions
All linear dimensions use the same unit. For “Known base area”, the area is interpreted in that unit squared.
Length of the base side of the triangular face.
Perpendicular height corresponding to the base b.
Length (or height) of the prism along which the triangular face is extruded.
All linear values (sides, height, length) are interpreted in this unit.
2. Triangular prism volume results
The calculator first computes the area of the triangular base, then multiplies by the prism length. Results are normalised to cubic metres and then converted into different units.
Volume of a triangular prism: formula and definitions
A triangular prism is a three-dimensional solid with two parallel, congruent triangular faces and three rectangular lateral faces. Its volume is given by
Right triangular prism: base and height known
If the triangular base is a right triangle with base \(b\) and corresponding height \(h\), its area is
This is the simplest case and is often encountered in school exercises and basic engineering problems. The calculator’s default mode “Right triangle: base & height” implements exactly this formula.
General triangular base: three sides and Heron’s formula
If the triangle is not right-angled and you only know its three sides \(a\), \(b\) and \(c\), you can still compute its area using Heron’s formula. First, compute the semiperimeter \(s = \frac{a + b + c}{2}\), then:
Once the base area is known, the volume follows from the usual prism formula:
The calculator’s “General triangle: three sides (Heron)” mode performs this sequence automatically and checks the triangle inequality to ensure that the sides form a valid triangle.
Known base area
In many practical tasks (for example, CAD outputs or technical datasheets) the area of the triangular face is given directly. In this case you simply have
where \(A_{\text{base}}\) is expressed in square units (e.g. cm²) and \(L\) in the corresponding linear unit (e.g. cm). The calculator converts this to cubic metres and other volume units.
Units and conversions
All linear dimensions are entered in the same unit. The calculator converts them to metres internally, computes the volume in m³ and then reports:
- Cubic millimetres (mm³) and cubic centimetres (cm³) – useful for small parts.
- Cubic metres (m³) – standard SI volume unit for engineering and logistics.
- Litres (L) – common for liquids and storage capacity (1 m³ = 1000 L).
- Cubic feet (ft³) – often used in international shipping and HVAC.
FAQ: triangular prism volume
1. Does the prism need to be “right”?
No. The formula \(V = A_{\text{base}} \cdot L\) holds for any prism whose cross-section is a congruent triangle along its length, regardless of whether the triangular base is right-angled or scalene. The only requirement is that the cross-section does not change along the length.
2. What if some data are missing?
To compute the volume you must know either:
- Base \(b\), height \(h\) of the triangle and prism length \(L\), or
- The three sides \(a\), \(b\), \(c\) of the triangle and \(L\), or
- The base area \(A_{\text{base}}\) and the length \(L\).
If you are missing some information, you may need additional geometric relationships (e.g. angles) to reconstruct the triangle.
3. Typical real-world applications
Triangular prisms appear in roof structures, trusses, concrete beams, storage containers, and many mechanical parts. The volume is directly related to:
- Material quantities (concrete, steel, wood, etc.).
- Weight estimates when combined with density.
- Container or channel capacity for fluids.
Formula (LaTeX) + variables + units
V = A_{\text{base}} \cdot L,
A_{\text{base}} = \frac{b \cdot h}{2}, \qquad V = \frac{b \cdot h}{2} \cdot L.
A_{\text{base}} = \sqrt{s(s-a)(s-b)(s-c)}.
V = A_{\text{base}} \cdot L.
','\
\[ V = A_{\text{base}} \cdot L, \] where \(A_{\text{base}}\) is the area of the triangular base and \(L\) is the length (or height) of the prism measured perpendicular to the base.
\[ A_{\text{base}} = \frac{b \cdot h}{2}, \qquad V = \frac{b \cdot h}{2} \cdot L. \]
\[ A_{\text{base}} = \sqrt{s(s-a)(s-b)(s-c)}. \]
\[ V = A_{\text{base}} \cdot L. \]
\[ V = A_{\text{base}} \cdot L, \]
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.