Volume of Triangular Prism Calculator

This calculator works out the volume of a triangular prism when you enter the base length, base height, and prism length (or depth). You get the volume in cubic units instantly, using the standard formula V = ½ × base × height × length. It also shows the same result in cubic centimeters, liters, and gallons so you can use it for math homework, construction, or packing estimates.

Formula

The volume of a triangular prism is the area of its triangular base multiplied by the prism’s length (the distance between the two triangular faces). In symbols:

V = ½ × b × h × l

• V = volume (cubic meters, cubic feet, etc.)
• b = base length of the triangular face (same unit as h)
• h = height of the triangular face, measured perpendicular to the base (same unit as b)
• l = length of the prism (the distance between the two triangular ends)

All three inputs must use the same unit. If you enter meters, the volume is in cubic meters. If you enter feet, the volume is in cubic feet. The calculator’s default values (b = 4 m, h = 3 m, l = 10 m) give a volume of 60 m³.

Worked Example

Using the default values from the calculator:

1. Base length b = 4 m
2. Base height h = 3 m
3. Prism length l = 10 m

First find the area of the triangular base: ½ × 4 × 3 = 6 m².

Then multiply by the prism length: 6 × 10 = 60 m³.

The calculator gives 60.00 m³, which matches. In liters, that is 60,000 L; in US gallons, it is about 15,850 gal.

When to Use the Triangular Prism Formula

Triangular prisms appear in real life more than you might think. Use this formula when you need the volume of:

• A triangular roof truss or a wedge-shaped concrete block
• A tent with a triangular cross-section
• A prism-shaped box or a triangular glass prism
• A channel or gutter with a triangular profile
• Any object that has the same triangular cross-section along its entire length

The key is that the triangular face must be identical at both ends and the sides must be rectangles. If the shape tapers or the ends are different, this formula does not apply.

How to Read the Result

The volume tells you how much space the prism occupies. In the example, 60 m³ is the space inside a prism 10 meters long with a triangular end that has a 4 m base and a 3 m height. That is roughly the size of a small room’s worth of air.

If you need the volume in different units, the calculator provides conversions:

• 1 m³ = 1,000 liters
• 1 m³ = 264.172 US gallons
• 1 ft³ = 7.48052 US gallons
• 1 ft³ = 28.3168 liters

For construction, you might need cubic yards of concrete. Divide cubic feet by 27 to get cubic yards. For example, 60 ft³ ÷ 27 ≈ 2.22 yd³.

Common Mistakes and How to Avoid Them

The most frequent error is mixing units. If the base is in centimeters and the length in meters, the result is meaningless. Convert everything to the same unit before calculating.

Another common mistake is using the slant height of the triangle instead of the perpendicular height. The “h” in the formula is the distance from the base to the opposite vertex, measured at a right angle to the base. If you only know the side lengths of the triangle, use Heron’s formula to find the area first, then multiply by the prism length.

Also, do not confuse the base height (of the triangle) with the prism length. The prism length is how long the prism is, not the height of the triangular face. In a tent, the prism length is the tent’s depth from front to back, while the base height is how tall the tent is at its peak.

Limits of the Formula

This formula works only for right prisms, where the triangular ends are parallel and the sides are rectangles perpendicular to the ends. If the prism is oblique (slanted), the volume is still the base area times the perpendicular distance between the ends, but the “length” you measure along the slant is not the correct value. Use the perpendicular distance instead.

The formula also assumes the triangular face is flat and the prism is solid. For a hollow triangular tube, you would need to subtract the inner volume from the outer volume. For a partially filled triangular container, the filled volume is a smaller triangular prism, so use the dimensions of the filled portion only.

Frequently Asked Questions

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

If you don’t have the base and height of the triangle, use Heron’s formula to get the area: first compute s = (a+b+c)/2, then area = √(s(s-a)(s-b)(s-c)). Multiply that area by the prism length to get the volume.

What units should I use?

Any consistent unit works. If you use centimeters for all three dimensions, the volume is in cubic centimeters. If you use feet, the volume is in cubic feet. The calculator defaults to meters but you can change the numbers to your unit.

Can I use this for a triangular swimming pool?

Yes, if the pool has a constant triangular cross-section along its length. Measure the triangle’s base and height at the shallow end (or the actual triangular profile) and the pool’s length. The result is the pool’s volume in cubic units, which you can convert to gallons or liters.

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

A triangular prism has two triangular bases and three rectangular sides. A triangular pyramid (tetrahedron) has one triangular base and three triangular sides that meet at a point. The volume formulas are different: prism volume = base area × length, pyramid volume = (1/3) × base area × height.

Why does the formula have ½ in it?

The ½ comes from the area of a triangle: area = ½ × base × height. A triangle is half of a rectangle with the same base and height. Since the prism volume is base area × length, the ½ carries through.

How do I convert cubic meters to liters?

Multiply cubic meters by 1,000. One cubic meter is exactly 1,000 liters. The calculator does this automatically in the second output.

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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 V | Volume | m³ | 0.5 * b * h * l | 2
out liters | Volume | L | (0.5 * b * h * l) * 1000 | 0
out gallons | Volume | US gal | (0.5 * b * h * l) * 264.172 | 1