Volume of a Triangular Prism: Formula & Calculator

This calculator finds the volume of a triangular prism. You enter the prism’s base length, base height, and prism length, and it returns the volume in cubic units. The formula is straightforward: Volume = (1/2 × base × height) × length, where the first part is the area of the triangular face.

Formula

The volume of a triangular prism is calculated by multiplying the area of its triangular base by the length (or height) of the prism. The formula is:

V = (1/2) × b × h × l

Where:

• V = Volume (cubic units, e.g., m³, cm³, ft³)
• b = Base length of the triangular face (units, e.g., m, cm, ft)
• h = Height of the triangular face (perpendicular distance from base to the opposite vertex, same units as b)
• l = Length of the prism (distance between the two triangular faces, same units as b and h)

Note that the base and height in the formula refer to the triangular face, not the overall prism. The “length” is how long the prism extends.

Worked Example

Using the default values from the calculator above:

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

First, find the area of the triangular face:

Area = (1/2) × b × h = (1/2) × 4 × 3 = 6 m²

Then multiply by the prism length:

Volume = 6 m² × 10 m = 60 m³

The calculator returns 60.00 m³, matching our manual calculation.

When to Use This Calculation

You need the volume of a triangular prism when dealing with objects that have a uniform triangular cross-section. Common real-world examples include:

• Concrete or soil in a triangular trench or channel
• Packaging, like a Toblerone-style box
• Roof spaces or attic volumes
• Water in a triangular weir or trough
• Any prism-shaped block in construction or manufacturing

If the object is not a perfect prism (e.g., a pyramid or a cone), this formula does not apply.

How to Read the Result

The volume is always in cubic units. If you input meters, you get cubic meters (m³); if you input centimeters, you get cubic centimeters (cm³). To convert to liters, remember 1 m³ = 1000 liters and 1 cm³ = 1 milliliter. For US customary units, 1 cubic foot ≈ 7.48 gallons.

For example, a volume of 60 m³ equals 60,000 liters. If the same dimensions were in feet, 60 ft³ would be about 449 gallons.

Common Mistakes and How to Avoid Them

• Mixing units: Ensure base length, base height, and prism length are all in the same unit before calculating. If not, convert first.
• Using the wrong height: The height in the formula is the perpendicular height of the triangular face, not the slant height or the prism length.
• Forgetting the 1/2 factor: The area of a triangle is half the base times height. Omitting this doubles your answer.
• Confusing with other prisms: For a rectangular prism, you simply multiply length × width × height. For a cylinder, use πr²h. Triangular prisms are specifically half of a rectangular prism with the same dimensions.

Limitations of the Formula

This formula works only for right prisms where the triangular faces are parallel and identical, and the side faces are rectangles. If the prism is oblique (slanted), the volume is still the area of the base times the perpendicular height (the distance between the two triangular faces), not the slanted length. In most practical cases, the prism is right, so the length you measure is the perpendicular height.

Also, the triangle can be any type—right, isosceles, equilateral, or scalene—as long as you know its base and perpendicular height. If you only know the three side lengths of the triangle, use Heron’s formula to find the area first, then multiply by the prism length.

Frequently Asked Questions

What is the formula for the volume of a triangular prism?

The formula is V = (1/2) × b × h × l, where b is the base of the triangular face, h is the height of the triangular face, and l is the length of the prism. It is the area of the triangle times the length.

How do I find the volume of a triangular prism without the height of the triangle?

If you know the three side lengths of the triangle, use Heron’s formula to find the area: s = (a+b+c)/2, Area = √(s(s-a)(s-b)(s-c)). Then multiply that area by the prism length.

What is the difference between a triangular prism and a triangular pyramid?

A triangular prism has two triangular bases and three rectangular faces, with a consistent cross-section along its length. A triangular pyramid (tetrahedron) has one triangular base and three triangular faces meeting at a point. Their volume formulas are different: prism = base area × height, pyramid = (1/3) × base area × height.

How do I convert cubic meters to liters for a triangular prism?

Multiply the volume in cubic meters by 1000 to get liters. For example, 60 m³ × 1000 = 60,000 liters. If your volume is in cubic centimeters, divide by 1000 to get liters.

Can I use this formula for a slanted (oblique) triangular prism?

Yes, but you must use the perpendicular distance between the two triangular faces as the length, not the slanted edge length. The volume is always base area × perpendicular height.

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