Volume of a Triangular Prism: Formula & Examples

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 instantly, with the formula and a worked example shown below.

Formula

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

V = (½ × b × h) × l

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

Notice that the first part, ½ × b × h, is just the standard area formula for a triangle. Once you have that area, you multiply by the prism’s length to get volume.

Worked Example

Using the default values from the calculator: base of triangle = 6 m, height of triangle = 4 m, length of prism = 10 m.

1. Calculate the area of the triangular base: ½ × 6 × 4 = 12 m².
2. Multiply by the length of the prism: 12 × 10 = 120 m³.

The volume is 120 cubic metres (120 m³). The calculator shows the same result, rounded to 2 decimal places.

When to Use This Calculation

Triangular prisms appear in everyday objects and construction. Common examples include:

• Roof trusses and gable ends of buildings
• Tent shapes (A-frame tents)
• Chocolate bar packaging with triangular cross-sections
• Concrete kerbs or drainage channels
• Prism-shaped glass blocks used in optics

If you need to know how much space is inside a triangular-shaped container, or how much concrete is needed for a triangular trough, this formula gives the exact volume.

How to Read the Result

The volume is always in cubic units. If you entered metres, the volume is cubic metres (m³). If you entered centimetres, you get cubic centimetres (cm³). One cubic metre equals 1,000 litres, which is useful when converting to liquid capacity. For example, the 120 m³ from the worked example equals 120,000 litres.

If you only need the area of the triangular face (for example, to paint the side), the second output gives that directly. The volume is the area of that face multiplied by how long the prism extends.

Common Mistakes and How to Avoid Them

The most frequent error is mixing up the triangle’s height with the prism’s length. The triangle’s height is the perpendicular distance from the base of the triangle to its opposite vertex. The prism’s length is the distance between the two triangular faces. They are different dimensions.

Another common mistake is using the slant height of the triangle instead of the perpendicular height. Always use the height that forms a right angle with the base of the triangle. If you only know the side lengths of the triangle, you may need to calculate the perpendicular height first using trigonometry (e.g., for an equilateral triangle with side a, the height is a × √3/2).

Unit consistency is also critical. All three measurements must be in the same unit before multiplying. If the base is in metres and the length is in centimetres, convert one to the other first.

Limits of the Formula

This formula works for any triangular prism, regardless of the triangle’s shape – right, isosceles, equilateral, or scalene. The only requirement is that the two triangular faces are parallel and congruent, and the sides connecting them are rectangles (or parallelograms for an oblique prism). For an oblique prism, the length l must be measured perpendicular to the triangular faces, not along the slanted edge.

The formula does not apply to other 3D shapes. For a rectangular prism (box), use length × width × height. For a cylinder, use πr²h. If the shape is not a prism (e.g., a pyramid), the volume formula is different (one-third of base area times height).

Frequently Asked Questions

How do I find the volume if I only know the triangle’s side lengths?

You first need to find the triangle’s area. Use Heron’s formula: s = (a+b+c)/2, then area = √(s(s-a)(s-b)(s-c)). Multiply that area by the prism’s length. This works for any triangle when you don’t have the perpendicular height.

What if the triangle is right-angled?

For a right triangle, the two legs are the base and height. So the area is simply (leg1 × leg2) / 2. Then multiply by the prism’s length. You don’t need to find a separate height.

Can I use this formula for a triangular prism that is tilted (oblique)?

Yes, as long as you measure the length perpendicular to the triangular faces. The volume of any prism is base area times the perpendicular distance between the two bases, regardless of tilt.

How do I convert cubic metres to litres?

Multiply the volume in cubic metres by 1,000. So 120 m³ = 120,000 litres. For cubic centimetres, divide by 1,000 to get litres (since 1,000 cm³ = 1 litre).

Why is the formula ½ × base × height × length, not just base × height × length?

The ½ comes from the area of a triangle. A triangle is half of a rectangle with the same base and height. Since you multiply that area by the length, the half carries through. Without it, you’d be calculating the volume of a rectangular prism, not a triangular one.

What units should I use for the answer?

Use cubic units matching your input. If all inputs are in feet, the volume is in cubic feet. If you mix units, convert everything to one unit first. The calculator assumes all three inputs are in the same unit.

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in b | Base of triangle | m | 6 | 0
in h | Height of triangle | m | 4 | 0
in l | Length of prism | m | 10 | 0
out v | Volume | m³ | (b * h / 2) * l | 2
out ba | Base triangle area | m² | b * h / 2 | 2