Triangular Prism Volume

Also known as volume of a triangular prism · gable volume

V = \tfrac{1}{2} b h_t L

Worked example: 3-4-5 triangle end, 2 m long → 12 m3 — press Try an example to run it live, then adjust anything.

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Triangular Prism Volume explained

A triangular prism is a triangle extruded along a straight line: a tent, a gable roof space, a wedge of cheese, a section of dredged spoil. Its volume is the triangular end area $\tfrac{1}{2}bh_t$ multiplied by the run $L$ . The subscript matters, because $h_t$ is the height of the triangle, measured perpendicular to its base, and has nothing to do with how tall the prism stands.

The formula is worth knowing for the attic. A house 10 m long with a gable 8 m wide rising 3 m to the ridge encloses $\tfrac{1}{2}(8)(3)(10) = 120$ m³ of air, which is exactly the number an insulation contractor or a ventilation designer needs. A handy check on your work: a 3-4-5 right triangle has area exactly 6, so any prism built on one should come out as six times its length.

Triangular Prism Volume formula

V = \tfrac{1}{2} b h_t L

Where

$V$ = Volume (L)
$b$ = Triangle base (m)
$h_t$ = Triangle height (m)
$L$ = Prism length (m)

Missing one of these? Work it out first, then come back

Volume — Cone Frustum Volume (Truncated Cone), Torus Volume
Triangle base — Area of a Triangle, Parallelogram Area
Triangle height — Area of a Triangle, Cone Frustum Volume (Truncated Cone)
Prism length — Rectangle Perimeter, Rectangle Diagonal