About the Triangular Prism Calculator
A triangular prism is a solid with two identical triangular ends joined by three rectangular faces — the shape of a tent, a Toblerone bar, a roof section, a ramp or a glass prism. This calculator takes the three side lengths of the triangular end and the length of the prism, and returns the volume, the total surface area, the triangle (base) area, the lateral area of the three rectangles and the triangle’s height on side a.
Because it uses the three sides, it works for any triangle — right, isosceles, equilateral or scalene — without needing to measure a height. That makes it practical for estimating the air volume of an A-frame tent or attic, the concrete in a wedge-shaped ramp or the material needed to cover a triangular roof.
Choose a length unit to see the volume in litres and US gallons. The three sides must form a real triangle: each side must be shorter than the other two combined.
With the default inputs, the volume is 60. Change any value above to recalculate instantly.
How to use the triangular prism calculator
- 1Measure the three sides of one triangular end.
- 2Measure the length of the prism between the two ends.
- 3Enter the values and choose your unit.
- 4Read the volume, surface area and capacity in litres.
Formula and method
The volume of any prism is the area of its cross-section times its length. Here the cross-section is a triangle, and its area comes from Heron’s formula using only the three side lengths and the semi-perimeter s — no height measurement needed. If you know a base and height instead, the triangle area is simply ½ × base × height.
The surface area is the two triangular ends plus three rectangles, one for each side of the triangle, each with width equal to that side and length L. Together the rectangles cover the triangle’s perimeter × L.
- a, b, c
- Side lengths of the triangular end
- s
- Semi-perimeter of the triangle
- L
- Length of the prism
- V, S
- Volume and total surface area
Worked examples
3-4-5 triangle, 10 long
The 3-4-5 right triangle has area ½ × 3 × 4 = 6, so the volume is 6 × 10 = 60 cubic units. The three rectangles cover (3 + 4 + 5) × 10 = 120 and the two ends add 12, giving 132.
A-frame tent: equilateral 2 m ends, 3 m long
Each equilateral end has area (√3/4) × 2² ≈ 1.732 m², so the tent encloses about 5.20 m³ (roughly 5,196 litres of air). Fabric for the whole shape, including floor, is about 21.46 m².
Isosceles 5-5-6 prism, 20 inches long
The 5-5-6 triangle has height 4 on its base of 6, so its area is 12 in² and the volume is 240 in³ — about 3.93 litres. The surface is 2 × 12 + 16 × 20 = 344 in².
Frequently asked questions
How do you find the volume of a triangular prism?+
Multiply the area of the triangular end by the prism length: V = ½ × b × h × L. For a triangle with base 3 and height 4 and a length of 10, V = 6 × 10 = 60 cubic units.
What is the surface area formula for a triangular prism?+
Surface area = 2 × (triangle area) + (a + b + c) × L. The first part covers the two ends and the second the three rectangular sides.
Can I use this if I only know the base and height of the triangle?+
For volume, yes: compute ½ × base × height and multiply by the length. For surface area you also need all three sides; for a right triangle the third side is √(base² + height²).
How many faces, edges and vertices does a triangular prism have?+
It has 5 faces (2 triangles and 3 rectangles), 9 edges and 6 vertices, which satisfies Euler’s formula F − E + V = 2.
Why does the calculator say my sides cannot form a triangle?+
By the triangle inequality, each side must be shorter than the other two combined. Sides of 2, 3 and 6 fail because 2 + 3 is less than 6.