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Triangular Prism Volume Calculator

Find the volume of a triangular prism.

How it is calculated

The tool uses V = ½ × b × h × L. b is the base of the triangle, h is the triangle's height measured perpendicular to that base, and L is the length of the prism, the distance along which the triangle is extended. All three must be in the same unit; the volume then comes out in that unit cubed (the tool labels it generically as units³) and is rounded to two decimals.

The three values must each be greater than zero, otherwise nothing is returned. The formula is exact for any triangle, right-angled or not, as long as h is the true perpendicular height and not a slanted side.

Worked example

Take a wedge with a triangle base of 3.5, a triangle height of 2.4 and a length of 12. The triangle's area is ½ × 3.5 × 2.4 = 4.2. Extending it over the length gives 4.2 × 12 = 50.4. The tool shows 50.40 units³. If the three sizes were in metres, that is 50.40 cubic metres.

Try this example →

Common mistakes

  • Using a slanted side instead of the perpendicular height. For a non-right triangle the sloping edge is longer than the height and overstates the volume.
  • Mixing units, for example a base in centimetres and a length in metres. Convert everything to one unit first.
  • Forgetting the ½. Base × height × length is the volume of the enclosing box, exactly twice the prism.
  • Confusing the prism's length with the triangle's own side. L is the extrusion distance, perpendicular to the triangular face.
  • Reading units³ as a fixed unit. It is a placeholder; if you entered millimetres the answer is in mm³.

About this calculator

This calculator finds the volume of a triangular prism — a solid with a constant triangular cross-section extruded along its length — using V = (½·b·h)·L, where ½·b·h is the area of the triangular base (base times height, halved) and L is the length the triangle is extended through. It's the same base-times-height logic used for any prism, applied to a triangular base instead of a rectangular one.

Builders and carpenters use it to calculate material for wedge-shaped structures like roof trusses, ramps, and gable ends; manufacturing and materials engineers use it to determine volume and weight for extruded triangular metal or plastic profiles; and geometry students use it as a standard example of extending 2D area formulas into 3D volume.

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Comments (1)

  • Editorial team

    The height here is the triangle's own height, measured at right angles to its base, and not the slanted side or the prism's length. On a roof gable or a wedge-shaped box, the sloping edge is longer than that height and will overstate the volume. For a quick check, a prism of the same base and length with a rectangle of b by h would hold exactly twice as much. What object are you measuring with it?

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