Volume of Triangular Prism Formula & Calculator

This calculator works out the volume of a triangular prism when you enter the prism’s height and the base triangle’s base and height. You get the volume in cubic units, plus the base area, using the standard formula. The tool accepts any consistent unit (cm, m, inches, feet) and the result is in those same units cubed.

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 words:

Volume = (base × triangle height ÷ 2) × prism height

In symbols:

V = (b × h_t ÷ 2) × H

• V – volume (cubic units: m³, cm³, ft³, etc.)
• b – length of one side of the triangle chosen as the base (same linear unit as H)
• h_t – perpendicular height of the triangle from that base to the opposite vertex (same unit)
• H – height of the prism, i.e. the distance between the two triangular faces (same unit)

The expression (b × h_t ÷ 2) is simply the area of a triangle. Multiplying that area by the prism’s height gives the volume because the prism is made of that triangle stacked along the prism height.

Worked Example

Using the default values from the calculator above:

• Triangle base (b) = 4 m
• Triangle height (h_t) = 3 m
• Prism height (H) = 10 m

Step 1 – find the base triangle area:

Area = (4 × 3) ÷ 2 = 12 ÷ 2 = 6 m²

Step 2 – multiply by the prism height:

Volume = 6 × 10 = 60 m³

The calculator returns 60.00 m³, matching the manual calculation.

When to Use This Formula

Use the triangular prism volume formula whenever you need the space inside a three‑dimensional object whose two ends are identical triangles and whose sides are rectangles. Real‑world examples include:

• Concrete for a triangular‑shaped ramp or retaining wall
• Water in a triangular trough or gutter
• Packaging with triangular cross‑section (e.g. Toblerone‑style boxes)
• Roof attic space when the gable end is a triangle

The formula works for any triangle – right, isosceles, equilateral, or scalene – as long as you know the base and the perpendicular height of that triangle. You do not need to know the side lengths or angles.

How to Read the Result

The volume is always in cubic units. If you input metres, the volume is cubic metres (m³). If you input inches, the result is cubic inches (in³). To convert to other common volume units:

• 1 m³ = 1,000 litres (L)
• 1 cm³ = 1 millilitre (mL)
• 1 ft³ ≈ 7.48052 US gallons
• 1 in³ ≈ 16.3871 cm³

For example, the 60 m³ from the worked example equals 60,000 litres. If you are calculating how much liquid a triangular tank holds, convert the cubic volume to litres or gallons using those factors.

Common Mistakes and How to Avoid Them

The most frequent errors when using this formula are:

• Mixing units – e.g. entering the base in metres and the height in centimetres. Convert all measurements to the same unit before calculating.
• Forgetting to divide by 2 – the triangle area requires the ½ factor; skipping it doubles the volume.
• Using the slant height instead of the perpendicular height of the triangle. The perpendicular height is measured at a right angle to the base, not along the sloping side.
• Confusing the prism height with the triangle height – the prism height is the distance between the two triangular faces, not the height of the triangle itself.
• Rounding too early – keep full precision until the final step, then round to the desired number of decimal places.

Another common misconception: the formula works even if the prism is oblique (leaning). As long as the cross‑section is a triangle and the prism has a constant cross‑section, the volume is still base area × prism height (measured perpendicular to the base).

Limits of the Formula

This formula applies only to triangular prisms – solids with two parallel, congruent triangular faces and three rectangular lateral faces. It does not apply to:

• Pyramids (triangular or otherwise) – those use ⅓ × base area × height
• Triangular wedges or tetrahedra – different formulas
• Shapes with non‑constant cross‑section (e.g. a cone or a curved trough)

If the object is not a true prism, the formula gives an approximation at best. Also, the triangle base must be a flat, two‑dimensional triangle; if the base is curved or warped, the area calculation changes.

Frequently Asked Questions

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

The formula is V = (b × h_t ÷ 2) × H, where b is the base of the triangle, h_t is the perpendicular height of the triangle, and H is the height of the prism (distance between the two triangular faces).

Can I use this formula if the triangle is not right‑angled?

Yes. The formula works for any triangle – right, isosceles, equilateral, or scalene – as long as you know the base and the perpendicular height of that triangle. You do not need the side lengths or angles.

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

You can use Heron’s formula to find the triangle’s area first, then multiply by the prism height. Heron’s formula: area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2. Once you have the area, multiply by the prism height to get the volume.

How do I convert the volume to litres or gallons?

After calculating the volume in cubic units, use conversion factors: 1 m³ = 1000 litres, 1 cm³ = 1 mL, 1 ft³ ≈ 7.48052 US gallons, 1 in³ ≈ 16.3871 cm³. For example, 60 m³ = 60,000 litres.

Does the prism have to be upright (right prism) for the formula to work?

No. Even if the prism leans (oblique prism), the volume is still base area × prism height, where the prism height is measured perpendicular to the base. The cross‑section must remain a triangle throughout.

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

A triangular prism has two triangular bases and three rectangular faces; its volume is base area × height. A triangular pyramid (tetrahedron) has one triangular base and three triangular faces meeting at a point; its volume is (1/3) × base area × height.

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in t | Prism height | m | 10 | 0
in b | Triangle base | m | 4 | 0
in h | Triangle height | m | 3 | 0
out vol | Volume | m³ | (b * h / 2) * t | 2
out base_area | Base area | m² | b * h / 2 | 2