Volume of a Triangular Prism: Formula & Examples

This calculator finds the volume of a triangular prism. You enter the base length, base height (the height of the triangle), and the prism length (the distance between the two triangular faces), and it returns the volume in cubic units. The formula is V = ½ × base length × base height × prism length.

Formula

The volume of any prism is the area of its cross-section multiplied by its length. For a triangular prism, the cross-section is a triangle, so:

V = ½ × b × h × l

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

All three lengths must be in the same unit before multiplying. If you mix metres and centimetres, the result will be wrong by a factor of 100 or 1,000,000.

Worked Example

Using the calculator defaults: base length = 6 m, base height = 4 m, prism length = 10 m.

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

The calculator shows 120.00 m³, matching the step-by-step result.

When to Use This Formula

Use this calculation whenever you need the space inside a shape with a triangular cross-section that stays the same along its length. Common real-world examples include:

• Concrete for a triangular channel or ramp
• Water in a triangular trough or gutter
• Packaging, like a Toblerone-style box
• Soil or gravel in a triangular prism-shaped pile

The formula works for any triangle – right, isosceles, scalene – as long as you know the base length and the perpendicular height. You do not need the side lengths.

How to Choose the Right Dimensions

The most common mistake is confusing the triangle height with the prism length. The triangle height is the perpendicular distance from the base to the opposite vertex, measured at 90° to the base. The prism length is the distance between the two identical triangular ends – often the longest dimension, like the length of a tent or a beam.

If the triangle is not right-angled, the height is not a side. For example, an equilateral triangle with side 4 cm has a height of 4 × (√3/2) ≈ 3.46 cm, not 4 cm. Use the perpendicular height, not the slant side.

Common Mistakes and How to Avoid Them

• Forgetting the ½: The area of a triangle is half the base times height. Skipping the ½ doubles your answer.
• Mixing units: Convert everything to the same unit first. If the base is in inches and the length in feet, convert feet to inches (or vice versa) before multiplying.
• Using the wrong height: The height must be perpendicular to the base, not the length of a slanted side.
• Rounding too early: If you round the triangle area to 2 decimal places before multiplying by a long length, the final volume can be noticeably off. Keep full precision until the last step.

Limits of the Formula

This formula assumes a perfect prism – the triangular faces are parallel and identical, and the sides are rectangles. If the shape tapers (like a wedge or a pyramid), this formula does not apply; you would need a different formula, often involving integration or the frustum formula. Also, the formula gives the mathematical volume, not the actual capacity of a container, which may be reduced by wall thickness, rounded corners, or internal fittings.

Frequently Asked Questions

What if the triangle is not right-angled?

The formula still works. You just need the base length and the perpendicular height from that base to the opposite vertex. You can find the height using trigonometry or by drawing the altitude, but you do not need the side lengths.

How do I convert the volume to litres?

1 m³ = 1,000 litres. So if your volume is 0.5 m³, that is 500 litres. For cubic centimetres, 1 cm³ = 1 millilitre, so 1,000 cm³ = 1 litre.

Can I use this for a tent or a roof?

Yes, if the tent or roof is a triangular prism. Measure the triangle’s base and height at the end, and the length of the tent. The volume is ½ × base × height × length. For a roof, this gives the air space under it, useful for ventilation or heating calculations.

What is the difference between surface area and volume?

Volume is the space inside the prism, measured in cubic units. Surface area is the total area of all five faces (two triangles and three rectangles), measured in square units. They answer different questions: how much it holds versus how much material covers it.

Why is the formula ½ × base × height × length?

Because the area of a triangle is ½ × base × height. A prism’s volume is the area of its cross-section times its length. So you multiply the triangle area by the prism length. The ½ comes from the triangle area, not from the prism.

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

You can use Heron’s formula to find the triangle area, then multiply by the prism length. Heron’s formula: area = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2. Then multiply that area by the prism length.

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in b | Base length | m | 6 | 0
in h | Base height | m | 4 | 0
in l | Prism length | m | 10 | 0
out V | Volume | m³ | 0.5 * b * h * l | 2