Triangular Prism Volume Calculator

A triangular prism has two parallel triangular ends and three rectangular sides connecting them. Toblerone bars, gabled rooflines and prism wedges are all the same shape.

V = (½ × b × h_t) × L

Where b is the triangle’s base, h_t is the triangle’s height (the perpendicular distance from base to opposite vertex, NOT a slant side), and L is the prism’s length (how long the bar is).

The (½ × b × h_t) part is just the triangle area, and L extends it into 3D.

Worked example: gable-end attic volume You have a gabled attic. The roof rises symmetrically, 24 ft wide at the floor and 8 ft tall at the peak.
The house is 40 ft long.
Triangle area = 0.5 × 24 × 8 = 96 sq ft.
Volume = 96 × 40 = 3,840 cubic feet of attic space.

That’s the unheated air volume an HVAC contractor needs to account for when sizing ductwork running through the attic, or what an insulator estimates when bagging cellulose.

Where triangular prisms appear in real measurements:

• Roof attic space. Most US homes have a gabled or hipped roof, so the attic is a triangular prism (gable) or a pair of them (hip).
• Ramp volumes for concrete pours. Wheelchair ramps and loading ramps are triangular prisms in cross-section. Need the concrete volume? It’s (½ × run × rise) × ramp width.
• Toblerone chocolate bars. The classic 100 g bar is roughly a 21 cm × 3 cm × 2.6 cm triangular prism.
• Glass optical prisms. Lab equipment for splitting light.
• Wedge cuts in landscaping. When you cut a triangular swale or ditch into a slope, the volume of soil removed is a triangular prism.

The “triangle height” gotcha:

The h in this formula is the triangle’s perpendicular height, NOT the length of a slanted side. For an equilateral triangle with side s, the perpendicular height from base to vertex is (s × √3)/2 ≈ 0.866 × s, about 13.4% shorter than the slant side.
Measure the slant by accident and the volume comes out roughly 15% high. Always project to the perpendicular.

If you already measured a slanted side and would rather not go back up on the roof, the real height is recoverable. For a symmetric triangle with base b and two equal slanted sides s:

h = √(s² − (b/2)²)

A 24 ft wide gable whose rafters measure 14.4 ft along the slope stands 8.0 ft at the peak, not 14.4. That one mistake nearly doubles an attic estimate. The calculator runs this check on every result and prints the corrected figure whenever the height you typed is long enough to have been a slanted side.

For a right-angled triangular prism (where the triangle has a 90° angle, like an attic with one vertical end): V = (½ × a × b) × L, where a and b are the two perpendicular legs.

Sanity check:

• Equal-sided triangle prism: works the same. Use the equilateral triangle area formula (s²√3 / 4) and multiply by L.
• Right triangle cross-section: works the same, since the area is half the product of the two legs.
• L = 0: V = 0 (zero-length prism is just a triangle). ✓
• The prism always fills exactly half its bounding box, b × h × L. Fastest sanity check there is.