Triangular Prism Volume Calculator

Base area × length with Heron support

Compute the volume of a triangular prism using the dimensions you actually know: base and height of the triangular face, its three sides (Heron’s formula), or the base area and prism length. The tool returns volume in multiple units and shows the formulas used.

Designed for students, teachers, engineers and logistics professionals who need fast, reliable volume calculations for triangular prisms.

1. Enter triangular prism dimensions

Input mode:

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.

Base area \(A_{\text{base}}\)
—
in m²
Volume (SI)
—
in cubic metres (m³)
Volume (selected unit³)
—
—
Volume in litres
—
1 m³ = 1,000 L
Volume in cm³
—
1 m³ = 1,000,000 cm³
Volume in ft³
—
1 m³ ≈ 35.3147 ft³

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

\[ V = A_{\text{base}} \cdot L, \] 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.

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

\[ A_{\text{base}} = \frac{b \cdot h}{2}, \qquad V = \frac{b \cdot h}{2} \cdot L. \]

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:

\[ A_{\text{base}} = \sqrt{s(s-a)(s-b)(s-c)}. \]

Once the base area is known, the volume follows from the usual prism formula:

\[ V = A_{\text{base}} \cdot L. \]

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

\[ V = A_{\text{base}} \cdot L, \]

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.