Volume of a Triangular Prism Calculator

Enter the triangular cross-section's base and height plus the prism's length to get the volume (V = ½ × base × height × length) and cross-sectional area.

Quick Facts

Volume formula
V = (½ × base × height) × length
The triangular cross-section's area, extruded along the prism's length.
Cross-section area
A = ½ × base × height
Use the triangle's perpendicular height, not a slanted side.
Surface area
SA = 2A + perimeter × length
Two triangular end caps plus three rectangular side faces.

Your Results

Calculated
Volume
-
V = cross-section area × length
Cross-Sectional Area
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A = ½ × base × height
Two End-Cap Area
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2 × cross-sectional area
Estimated Fill/Material Cost
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Volume × cost per cubic unit

Ready

Enter the triangle's base, height, and the prism's length, then press Calculate.

Formula and Method for the Volume of a Triangular Prism

A triangular prism is a solid with two parallel, congruent triangular faces (the "ends") connected by three rectangular faces. Its volume is the area of the triangular cross-section multiplied by the prism's length: V = (½ × base × height) × length, where base and height describe the triangle and length is the distance between the two triangular ends. This calculator also reports the cross-sectional area and the combined area of both triangular end caps, plus an optional material or fill cost estimate.

How the calculation works

Enter the triangle's base and its perpendicular height — the straight-line distance from the base to the opposite vertex, not a slanted side — along with the prism's length, and choose the unit they're measured in. The calculator first finds the cross-sectional area with A = ½ × base × height (in square units, such as ft² or m²), then multiplies that area by the prism's length to get the volume (in cubic units, such as ft³ or m³). If you enter a cost per cubic unit, the tool multiplies it by the volume to estimate total material or fill cost.

Common mistakes

  • Using a slant side instead of the height: the triangle's height must be measured perpendicular to the base. Using a slanted edge instead overstates the cross-sectional area.
  • Confusing the triangle's height with the prism's length: the height stays inside the flat triangular face; the length runs the other direction, connecting the two triangular ends.
  • Mixing units: keep base, height, and length in the same unit — convert inches to feet, or centimeters to meters, before entering values.

Real-world applications

  • Concrete wedges, ramps, and roof trusses use triangular-prism volume to estimate material quantities.
  • Water troughs, awnings, and tent shapes with a triangular cross-section use this formula to size capacity.
  • Packaging and shipping (triangular-cross-section boxes or Toblerone-style containers) use it to compute fill volume.
  • Engineering and construction combine volume with a cost or density figure to estimate material weight or budget before ordering.

Frequently Asked Questions

What is the formula for the volume of a triangular prism?
Volume equals the area of the triangular cross-section times the prism's length: V = (½ × base × height) × length. For example, a triangle with a 6 ft base and 4 ft height has an area of 12 ft²; multiplied by a 10 ft prism length gives a volume of 120 ft³.
What is the difference between the triangle's height and the prism's length?
The triangle's height is the perpendicular distance from the base to the opposite vertex, measured within the flat triangular cross-section. The prism's length (sometimes called depth) is the distance between the two parallel triangular end faces, running perpendicular to that cross-section.
How do I find the volume if I only know the three side lengths of the triangle?
Use Heron's formula to get the triangle's area from its three sides a, b, c: compute the semi-perimeter s = (a + b + c) / 2, then Area = √(s(s-a)(s-b)(s-c)). Multiply that area by the prism's length to get the volume.
How do you calculate the surface area of a triangular prism?
Total surface area equals twice the triangular cross-sectional area (the two end caps) plus the perimeter of the triangle times the prism's length (the three rectangular side faces): SA = 2 × Area + (a + b + c) × length, where a, b, and c are the triangle's three side lengths.

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