Find the volume and surface area of a triangular prism. Choose how you want to describe the triangular base — from its base and height, three sides, and more — enter the prism length, and the calculator does the rest.
The triangular prism calculator works out the volume and surface area of a triangular prism — a solid with two identical triangular ends joined by three rectangular faces. Because the triangular base can be described in several ways, the calculator lets you choose the method that matches the measurements you have: base and height, a right triangle, three sides, two sides and the angle between them, two angles and the side between them, or simply the area of the triangular face. Enter your base measurements and the prism's length, and it returns the base area, the volume, and (whenever the full triangle is known) the surface area, in any unit you like.
This page explains what a triangular prism is, the formulas for its volume and surface area, how each base-definition method works, worked examples you can reproduce, and answers to the questions people ask most. Whether you are sizing a tent, a ramp, a length of moulding, or a piece of chocolate, this tool has you covered.
A triangular prism is a three-dimensional solid with two parallel, identical triangular bases connected by three rectangular (or, in an oblique prism, parallelogram) faces. It has the same triangular cross-section along its entire length, which is exactly what makes its volume easy to calculate. Everyday examples include camping tents, the classic Toblerone chocolate bar, glass prisms that split light into a rainbow, wheelchair ramps, and many roof trusses. The two triangular ends are called the bases, and the distance between them — the length of the prism — is sometimes called the height of the prism (not to be confused with the height of the triangle itself).
The volume of any prism is the area of its base times its length, and a triangular prism is no exception:
volume = base area × length
where the base area is the area of the triangular end and the length is the distance between the two triangular faces. If you know the triangle's base b and height h, the base area is ½ × b × h, so the volume becomes:
volume = 0.5 × b × h × length
When you know the three sides of the base triangle instead, the calculator uses Heron's formula to find the base area, then multiplies by the length.
The surface area is the total area of all five faces: the two triangular bases plus the three rectangles that wrap around the sides. Each rectangle has one side equal to the prism length and the other equal to one side of the triangle, so together the three rectangles have an area of length times the triangle's perimeter. Adding the two triangular ends gives:
surface area = length × (a + b + c) + 2 × base area
where a, b, and c are the three sides of the base triangle. This is why the surface area needs the full triangle: you have to know all three sides to find the perimeter. If you only supply the base and height, or just the area of the face, the calculator can still give the volume but not the surface area.
Imagine a ridge tent whose triangular cross-section has sides of 60, 50, and 50 inches, and which is 80 inches long. First, the base area from Heron's formula. The semi-perimeter is s = (60 + 50 + 50) / 2 = 80, so:
base area = √(80 × (80−60) × (80−50) × (80−50)) = √(80 × 20 × 30 × 30) = √1,440,000 = 1,200 in²
Then the volume and surface area:
volume = 1,200 × 80 = 96,000 cu in (about 55.56 cu ft)
surface area = 80 × (60 + 50 + 50) + 2 × 1,200 = 12,800 + 2,400 = 15,200 in²
So the tent encloses 96,000 cubic inches of space and has 15,200 square inches of fabric-and-floor surface. These are the calculator's default values, so you can press Calculate to confirm them, then change the numbers or the method to suit your own prism.
The triangular base can be measured in different ways, and the calculator supports six of them:
When you know the three sides of a triangle but not its height, Heron's formula gives the area directly. First compute the semi-perimeter, s = (a + b + c) / 2, then the area is the square root of s(s−a)(s−b)(s−c). It works for any triangle and is the backbone of the three-sides method in this calculator. An equivalent form, used internally, is area = ¼ × √((a+b+c)(−a+b+c)(a−b+c)(a+b−c)), which avoids computing the semi-perimeter separately. For the calculation to be valid the three sides must satisfy the triangle inequality — each side must be shorter than the sum of the other two — otherwise no triangle exists and the calculator will let you know.
The shape of the base triangle gives the prism its character. A right triangular prism has a right triangle as its base, common in ramps and wedge shapes; you only need the two legs, and the calculator finds the hypotenuse for you. An isosceles triangular prism has a base with two equal sides — the classic tent or Toblerone shape — symmetric and stable. An equilateral triangular prism has all three base sides equal, giving a particularly elegant, uniform solid often seen in optical prisms. Whatever the base, the volume is always base area times length, and the surface area is always length times perimeter plus the two triangular ends; only the way you compute the base area changes.
The calculator lets you work in millimeters, centimeters, meters, inches, feet, or yards, and it keeps everything consistent: all your length inputs use the same unit, the volume comes out in the corresponding cubic unit, and the surface area in the corresponding square unit. If you enter inches, the volume is in cubic inches and the surface area in square inches, just like the tent example. To convert to other units afterwards, remember that there are 1,728 cubic inches in a cubic foot and 144 square inches in a square foot, so the tent's 96,000 cubic inches equal about 55.56 cubic feet and its 15,200 square inches equal about 105.56 square feet. Working in a single consistent unit avoids the most common source of error in volume and area calculations.
Triangular prism calculations show up in many practical situations. Campers and tent makers use the volume to gauge interior space and the surface area to estimate fabric. Builders calculate the volume of triangular ramps, wedges, and gable roof sections, and the surface area for cladding or waterproofing. Manufacturers of everything from chocolate bars to structural beams rely on these formulas for material estimates. Students meet triangular prisms throughout geometry, and physics students study glass prisms that refract and disperse light. Landscapers compute the volume of triangular garden beds or drainage channels. In each case, breaking the problem into "find the triangle's area, then multiply by the length" makes it straightforward — and this calculator handles the arithmetic instantly.
The single most common mistake with triangular prisms is mixing up the two "height-like" measurements. A triangular prism has the height of its triangular face — the perpendicular distance from the base of the triangle to its opposite vertex — and the length of the prism, which is the distance between the two triangular ends. In the volume formula, the triangle's height helps find the base area, while the prism length is what you multiply that area by. To make matters worse, some textbooks call the prism length the "height of the prism," especially when the prism stands upright. Whenever you calculate, be clear about which dimension is which: the area of the triangular face uses the triangle's own measurements, and the length is always the third dimension that gives the prism its depth. This calculator keeps them separate — the base-triangle fields describe the face, and the prism length field is distinct — so you are far less likely to slip up.
A helpful way to understand the surface area is to picture the prism's net — the flat shape you would get by unfolding it. A triangular prism unfolds into two triangles (the identical ends) and three rectangles (the sides that wrap around). Each rectangle shares the prism's length as one dimension and one side of the triangle as the other, which is exactly why the three rectangles together have an area of length times the triangle's perimeter. Laying the net out flat makes the surface-area formula intuitive: you are simply adding the areas of five flat shapes. Nets are also practical — if you are cutting fabric for a tent, sheet metal for a wedge, or card for a model, the net tells you the exact shapes and sizes to cut, and the total area tells you how much material you need before adding seams or overlaps.
Multiply the area of the triangular base by the length of the prism: volume = base area × length. For a base area of 1,200 in² and a length of 80 in, the volume is 96,000 cubic inches.
Add the areas of all five faces: surface area = length × (a + b + c) + 2 × base area, where a, b, and c are the three sides of the triangle.
The surface area needs the perimeter of the triangle, which requires all three sides. Base and height fix the area but not the two slanted sides, so only the volume can be found.
Heron's formula finds a triangle's area from its three sides: with s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)). The calculator uses it for the three-sides method.
The triangle's height is a measurement of the triangular face; the prism's length (sometimes called its height) is the distance between the two triangular faces. They are different dimensions.
The volume formula (base area × length) holds for oblique prisms too, using the perpendicular length. The surface-area formula here assumes a right prism with rectangular side faces.
This Triangular Prism Calculator is provided for general educational purposes. It computes the volume and surface area of a right triangular prism from the values you enter. Confirm measurements and, for construction or manufacturing, allow for real-world tolerances and material thickness.