Triangular Prism Volume Formula & Calculator

This calculator works out the volume of a triangular prism from the base triangle’s base and height and the prism’s length. You enter those three measurements, and you get the volume in cubic units. The result uses the standard formula V = ½ × base × triangle height × prism length.

Formula

Volume = ½ × b × h × l

Where:

• b = length of the base edge of the triangular face (m)
• h = perpendicular height of the triangular face from the base to the opposite vertex (m)
• l = length of the prism, measured perpendicular to the triangular face (m)

The result is in cubic meters (m³) if all inputs are in meters. Use consistent units: if you enter centimeters, the volume is in cubic centimeters; if feet, cubic feet.

Worked Example

Using the default values: base b = 4 m, triangle height h = 3 m, prism length l = 10 m.

1. Multiply base by height: 4 × 3 = 12
2. Take half: 12 × ½ = 6
3. Multiply by length: 6 × 10 = 60

Volume = 60 m³. The calculator shows 60.00 m³.

Why the ½ Appears

A triangular prism is a stack of identical triangles. The area of one triangle is ½ × base × height. Multiplying that area by the prism’s length gives the volume. This works for any triangle – right, isosceles, scalene – as long as you use the perpendicular height, not a slanted side.

When to Use This Calculator

Use it for physical objects shaped like a triangular prism: tent volumes, wedge-shaped concrete forms, prism-shaped containers, or triangular roof spaces. It is also a common geometry homework problem. If you have the triangle’s three side lengths but not the height, you can find the height using Heron’s formula first, then apply this volume formula.

Common Mistakes

• Using the wrong height: The height must be perpendicular to the base of the triangle, not the length of a slanted side.
• Unit mismatch: Mixing meters and centimeters gives nonsense. Convert all to the same unit first.
• Forgetting the ½: Some people compute base × height × length, which gives double the correct volume.
• Confusing prism length with triangle side: The prism length is the distance between the two triangular faces, not a side of the triangle.

Limitations of the Formula

This formula assumes the prism is a right prism – the triangular faces are parallel and the length is perpendicular to them. For an oblique prism (slanted), the volume is still base area × perpendicular height between the faces, which is not the same as the slant length. Also, the triangle must be a flat, two-dimensional shape; any curvature or irregularity changes the volume.

Frequently Asked Questions

What if the triangle is not right-angled?

The formula works for any triangle. You just need the perpendicular height from the base to the opposite vertex. If you only know the side lengths, use Heron’s formula to find the area, then multiply by the prism length.

How do I convert volume to liters?

1 liter = 1000 cubic centimeters. If your volume is in cubic meters, multiply by 1000 to get liters (1 m³ = 1000 L). For cubic centimeters, divide by 1000.

Can I use this for a tent?

Yes, if the tent is a triangular prism shape. Measure the base width of the triangular end, the height from ground to peak, and the length of the tent. The volume gives the interior space in cubic units.

What is the difference between a prism and a pyramid?

A prism has two identical parallel faces (bases) connected by rectangles. A pyramid has one base and a single apex point. The volume formulas differ: prism volume = base area × height; pyramid volume = (1/3) × base area × height.

Why does the formula use ½ and not another fraction?

Because the area of a triangle is exactly half the area of a rectangle with the same base and height. A triangle is half of a rectangle, so the ½ is fundamental to the shape, not an approximation.

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in b | Base of triangle | m | 4 | 0
in h | Height of triangle | m | 3 | 0
in l | Length of prism | m | 10 | 0
out V | Volume | m³ | 0.5 * b * h * l | 2