Volume of a Prism Calculator

Volume of a triangular prism formula

Every prism, whatever the shape of its ends, has the same volume rule: the area of one end face times the distance between the two ends. For a triangular prism the end face is a triangle, so the area is half the base times the height of that triangle.

V = ½ × b × h × Lb and h are the base and height of the triangular face, L is the length of the prism.

Written another way, V = (area of the triangle) × L. Because all three measurements are multiplied together, doubling any one of them doubles the volume.

What the three measurements mean

• Prism length (L): the distance between the two triangular ends, measured along the prism.
• Prism base (b): one side of the triangular end, chosen as the base.
• Prism height (h): the perpendicular distance from that base to the opposite corner of the triangle. It must meet the base at a right angle, so it is not the length of a slanted side unless the triangle has a right angle there.

For a right-angled triangular end, the two legs are the base and the height. Need the triangle's area on its own? Use the triangle area calculator.

How to calculate the volume of a triangular prism

1. Measure the base and the perpendicular height of the triangular face.
2. Measure the length of the prism.
3. Enter the three values and choose the unit they share.
4. Press Calculate. The volume is returned in that unit cubed and rounded to six decimal places.

The calculator applies the unit you pick to all three inputs and to the answer. It does not convert between units, so measure everything in the same one.

Example: find the volume of a prism

A small wedge. Length 3 cm, base 4 cm and height 5 cm. The triangle has area ½ × 4 × 5 = 10 cm², so V = 10 × 3 = 30 cm³.

A loft space. The cross-section under a pitched roof is a triangle 8 m wide and 2.5 m high, and the loft runs for 12 m. V = ½ × 8 × 2.5 × 12 = 120 m³, which is 120,000 litres of air to heat.

A tent. A ridge tent has a triangular end 2 m wide and 1.2 m high and is 3 m long: V = ½ × 2 × 1.2 × 3 = 3.6 m³ of living space.

An equilateral prism. A chocolate bar with an equilateral triangle of side 3 cm has a triangle height of 3 × √3 ÷ 2 ≈ 2.598 cm. With a length of 20 cm, V = ½ × 3 × 2.598 × 20 ≈ 77.94 cm³.

All values in the table share one unit, so the volume is that unit cubed. Notice the third and fourth rows: very different shapes can hold the same volume.

Finding a missing dimension

If you know the volume and two of the three measurements, solve for the third. The length, for instance, is

L = 2 × V ÷ (b × h)

A prism of 90 m³ whose triangular face has a base of 6 m and a height of 5 m has a length of 2 × 90 ÷ 30 = 6 m. In the same way, h = 2V ÷ (b × L) and b = 2V ÷ (h × L).

Practical applications

• Building: the volume of a gable roof space, a ramp, a triangular concrete footing or a wedge-shaped planter.
• Packaging and design: prism-shaped boxes, tubes and desktop signs.
• Outdoors: tents, awnings and the air inside a lean-to.
• Optics and physics: glass prisms, where the volume feeds into mass and cost.

For other solids, try the box volume calculator, the cone volume calculator or the general volume calculator. To cover a prism with paint or material, the surface area calculator is the next step.

Common mistakes

• Using a slanted side of the triangle as its height. Only the perpendicular height gives the correct area.
• Leaving out the factor of one half, which doubles the result.
• Mixing the prism length with the triangle's base. They are different dimensions even though the labels sound similar.
• Entering some values in centimetres and others in metres. Convert everything to a single unit first.