Triangular Prism Volume Calculator
Pick the method that matches what you know about the triangular end. Get volume, surface area, and liquid capacity in one go.
A Toblerone bar. A tent. A water trough. A roof truss. All of them are triangular prisms — two matching triangle ends, connected by three flat rectangular sides. The math is simpler than it looks, once you know one thing: a triangular prism’s volume is just the triangle’s area, multiplied straight through by how long the prism is.
The Triangular Prism Volume Formula
\(V=\text{Base Area}\times\text{Length}\)
That’s the whole idea. Find the area of the triangular end — the same way you’d find any triangle’s area — then multiply by how far that shape extends. The only real decision is which method to use for the triangle’s area, and that depends on what you actually measured.
Method 1: Base & Height (The Fast One)
If you know the triangle’s base and its height, this is the quickest path:
\(V=\left(\frac{1}{2}\times b\times h\right)\times L\)
Worked Example
Base 5 units, height 6 units, prism length 7 units.
Base area: \(0.5\times5\times6=15\). Volume: \(15\times7=105\) cubic units.
One honest limitation: base and height alone don’t tell you the length of the triangle’s other two sides — there are endless triangles with the same base and height but different slanted sides. That means this method gives you volume, but not surface area. For that, one of the next three methods.
Method 2: Three Sides (Heron’s Formula)
Know all three side lengths of the triangular end? Heron’s formula finds the area without needing height at all — and since you already have all three sides, surface area comes along for free too.
\(\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}\), where \(s=\frac{a+b+c}{2}\)
Worked Example
Sides 3, 4, and 5 units, prism length 10 units — a classic right triangle.
Semi-perimeter: \(s=6\). Area: \(\sqrt{6\times3\times2\times1}=6\) sq units. Volume: \(6\times10=60\) cu units.
Surface area adds the two triangular ends to the three rectangular sides: \(2\times6+(3+4+5)\times10=12+120=132\) sq units.
Method 3: Two Sides + Included Angle
Know two sides and the angle squeezed between them? The Law of Cosines finds the third side, and from there it’s the same as the three-sides method — full volume and surface area.
\(\text{Area}=\frac{1}{2}ab\sin(C)\)
Run the same 3-4-5 triangle through this method instead — sides 3 and 4, with a 90° angle between them — and it lands on the exact same answer: area 6, volume 60, surface area 132. Different starting information, same triangle, same result. That agreement is exactly what confirms the math is internally consistent, not just separately plausible.
Method 4: Right Triangle (Two Legs)
If the triangular end is a right triangle and you know the two legs, the Pythagorean theorem finds the hypotenuse, and you’re set up for full volume and surface area — same idea as the last two methods, just a shortcut for the right-angle case.
\(\text{Hypotenuse}=\sqrt{\text{leg}_1^2+\text{leg}_2^2}\)
What About Liquid Capacity?
A prism-shaped water trough, an aquarium with an angled front panel, a chocolate mold — these hold liquid or pourable material, and cubic feet doesn’t mean much to most people at a glance. The calculator converts your volume straight into gallons and liters too, so you’re not doing that math separately.
A Word on “Right” vs. “Oblique” Prisms
Every formula here assumes a right triangular prism — one where the two triangular ends sit directly across from each other, with rectangular (not slanted) sides connecting them. That covers the overwhelming majority of real objects: tents, Toblerone bars, roof trusses, troughs. An oblique prism — where the ends are offset, like a leaning stack of triangular slices — needs a more advanced approach and isn’t covered here. If you’re not sure which one you have, picture the prism sitting upright with square-cut ends: if that matches your shape, you’re in the right place.
Where This Actually Comes Up
Architecture and roofing. Roof trusses and A-frame structures are triangular prisms end to end — volume matters for material and insulation estimates.
Civil engineering. Water troughs, drainage channels, and some bridge supports use this exact shape.
Packaging. The Toblerone bar is the textbook example for a reason — triangular-prism packaging is a real, recognizable design choice.
Tents and temporary structures. A-frame tents are triangular prisms, and their usable volume follows this same formula.
Frequently Asked Questions
Volume = base area × length, where the base area is the area of the triangular end and length is the distance between the two triangular ends. The triangle’s area can be found using base and height, three sides (Heron’s formula), two sides and an angle, or right-triangle legs.
No. Base and height alone don’t determine the triangle’s other two side lengths, which are needed for the rectangular side faces. Use the three-sides, two-sides-plus-angle, or right-triangle method instead to get surface area along with volume.
Total surface area = 2 × (triangle base area) + (triangle’s perimeter × prism length). The two triangular ends plus the three rectangular sides make up the full surface.
Multiply the volume in cubic feet by 7.48052 to get US gallons, or by 28.3168 to get liters. This calculator does the conversion automatically alongside the cubic-unit result.
No, this calculator assumes a right triangular prism, where the two triangular ends line up directly across from each other. An oblique prism, where the ends are offset, needs more advanced treatment than a straightforward formula can give.
Bottom Line
Every triangular prism problem comes down to one idea: find the triangle, multiply by the length. Four different starting points all lead there — pick the one that matches what you actually measured, and the rest follows.