Triangular Prism Volume Formula & Calculator

This calculator works out the volume of a triangular prism when you enter the base length, base height, and prism length (or height). It returns the volume in cubic units, using the standard formula V = ½ × base × triangle height × prism length.

Formula

The volume of a triangular prism is the area of its triangular base multiplied by the prism’s length (the distance between the two triangular faces). In symbols:

V = ½ × b × h × l

• V = volume (cubic units, e.g., m³, cm³, ft³)
• b = base length of the triangle (same unit as h and l)
• h = height of the triangle, measured perpendicular to the base (same unit)
• l = length of the prism (the distance between the two triangular faces)

Notice that ½ × b × h is the area of the triangle. So you can also think of it as: area of triangle × length of prism.

Worked Example

Using the default values from the calculator above:

• Base length (b) = 4 m
• Triangle height (h) = 3 m
• Prism length (l) = 10 m

First, find the area of the triangular base:

Area = ½ × 4 × 3 = 6 m²

Then multiply by the prism length:

Volume = 6 × 10 = 60 m³

The calculator gives the same result: 60.00 m³.

When to Use This Formula

Use this formula whenever you need the space inside a shape that has a triangle at both ends and straight sides connecting them – like a tent, a wedge, a prism-shaped box, or a triangular channel. It applies to any prism where the two end faces are identical triangles, whether the triangle is right-angled, isosceles, or scalene. The only requirement is that the triangle height is measured perpendicular to its base.

This is a common calculation in geometry classes, construction (estimating concrete for a triangular footing), packaging design, and fluid volume for tanks with triangular cross-sections.

How to Read the Result

The volume is always in cubic units. If you enter metres, you get cubic metres (m³). If you enter centimetres, you get cubic centimetres (cm³). One cubic metre equals 1,000 litres – useful if you’re thinking about water or other liquids. Similarly, 1 cm³ equals 1 millilitre.

For example, a prism with a base area of 6 m² and length 10 m holds 60 m³ of space, which is 60,000 litres.

Common Mistakes and How to Avoid Them

• Mixing units – Always convert all three measurements to the same unit before calculating. If base is in cm and length in m, convert one of them first.
• Using the wrong triangle height – The height must be the perpendicular distance from the base to the opposite vertex, not the length of a slanted side. For a right triangle, it’s the vertical leg; for others, you may need to measure or calculate it.
• Forgetting the ½ – The most common error is leaving out the ½ factor, which doubles the volume. Always remember the triangle area formula includes ½.
• Confusing prism length with triangle height – The prism length is the distance between the two triangular faces, not the height of the triangle itself. In a tent, the triangle height is the tent’s height; the prism length is the tent’s depth.

Limitations of the Formula

This formula works only for a right prism – one where the sides are perpendicular to the triangular faces. If the prism is slanted (an oblique prism), the volume is still base area × perpendicular height, but the perpendicular height is not the same as the slant length. In that case, you need the vertical distance between the two triangular faces, not the slanted edge length.

Also, the triangle must be flat – this formula does not apply to curved shapes or cones. For a cone or pyramid, you’d use a different formula (one-third of base area × height).

Frequently Asked Questions

What if the triangle is not right-angled?

It doesn’t matter. The formula ½ × base × height works for any triangle, as long as you use the perpendicular height. For an equilateral triangle, you can find the height using h = (√3/2) × side length. For a scalene triangle, you may need to calculate the height using trigonometry (e.g., h = side × sin(angle)) or Heron’s formula for the area first.

Can I use this formula for a triangular pyramid?

No. A pyramid has one triangular base and comes to a point, not a second triangle. Its volume is ⅓ × base area × height. This calculator is only for prisms, which have two identical triangular ends.

How do I convert cubic metres to litres?

Multiply by 1,000. One cubic metre equals 1,000 litres. So 60 m³ = 60,000 litres. Similarly, 1 cm³ = 1 mL, so 60 cm³ = 60 mL.

What if I only know the side lengths of the triangle?

You can find the triangle’s area using Heron’s formula: s = (a+b+c)/2, then area = √(s(s-a)(s-b)(s-c)). Once you have the area, multiply by the prism length to get the volume. You don’t need the height separately.

Does the order of multiplication matter?

No. Multiplication is commutative, so ½ × b × h × l gives the same result in any order. You can multiply the base and height first, or the base and length first – the answer is identical.

Why is the answer in cubic units?

Because volume measures three-dimensional space. You’re multiplying three lengths together (base, height, length), so the unit is cubed. If all three are in metres, the result is cubic metres (m³).

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in b | Base length | m | 4 | 0
in h | Triangle height | m | 3 | 0
in l | Prism length | m | 10 | 0
out vol | Volume | m³ | 0.5 * b * h * l | 2
out area | Base area | m² | 0.5 * b * h | 2