A triangular prism is a solid with two identical triangles at its ends joined by three rectangles: think of a tent, a Toblerone bar, a roof attic or a doorstop wedge. Its volume depends only on the area of the triangle and the length, but its surface needs the full shape of the triangle. This calculator works from whichever description of the triangle you have and reports the volume, capacity, every face area and the triangle’s angles.
How to use the triangular prism calculator
- Under The triangle end is given by, pick Three sides, Two sides and the angle between them, Right triangle: two legs, or Base and height (volume only).
- Enter the triangle’s measurements and the Prism length (L), the distance between the two triangular ends.
- Pick the Units (and the Angle unit if you entered an angle).
- Read the volume, capacity in liters and US gallons, total surface area, the end triangle area, the three rectangular faces, the base perimeter and the triangle’s angles. A diagram shows the prism with your labels.
Triangular prism formulas
The end area B comes from whichever rule fits your inputs:
| You know | Triangle area B |
|---|---|
| Base b and height h | ½bh |
| Three sides a, b, c | Heron: √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2 |
| Two sides and the angle C between them | ½ab sin C |
| Two legs of a right triangle | ½ab |
For the two-sides-and-angle option the third side is found first with the law of cosines, c = √(a² + b² − 2ab cos C), so every face can be measured.
Worked example: fabric for a ridge tent
A tent has a floor 6 ft wide and 8 ft long, and each sloping wall is 5 ft from floor to ridge.
Choose Three sides and enter a = 6, b = 5, c = 5 and L = 8 (feet).
- End triangle: s = 8, so B = √(8 × 2 × 3 × 3) = 12 ft². The ridge stands 4 ft high.
- Volume: 12 × 8 = 96 ft³ of space, about 2,718 liters of air.
- Faces: the floor is 6 × 8 = 48 ft² and each wall is 5 × 8 = 40 ft².
- Total surface: 2 × 12 + 128 = 152 ft². Leave out the floor and the tent body needs 152 − 48 = 104 ft² of fabric before seams.
Choosing the right input option
When you only know base and height
The Base and height option gives the volume and the end area, which is all you need to fill a trough or pour a wedge of concrete. It cannot give the surface area, because many different triangles share the same base and height; a tall, lopsided triangle has longer sloping sides than a symmetric one. Measure the slanted sides and switch to Three sides when you need material for the faces.
Right-triangle wedges
Ramps, doorstops, roof crickets and wheel chocks are right triangular prisms. With legs of 1.5 ft and 2 ft and a width of 10 ft, the hypotenuse is 2.5 ft, the volume is 15 ft³ and the three rectangular faces are 15, 20 and 25 ft², for a total surface of 63 ft² including both ends.
Two sides and an angle
Roof trusses and A-frames are often specified by rafter lengths and the angle at the peak. Two 4-inch sides meeting at 120° and extruded 12 inches give a third side of 6.928 in, an end area of 6.928 in² and a volume of 83.14 in³.
Tips and common mistakes
- L is the distance between the triangles, not the length of a triangle side.
- The height in ½bh must be perpendicular to the base. A slanted side is longer and overstates the volume.
- Three sides must satisfy the triangle inequality: the two shorter sides must add up to more than the longest. The calculator stops with a message if they do not.
- Converting capacity: 1 ft³ ≈ 7.48 US gallons and 1 ft³ ≈ 28.32 liters, which the results apply for you.
For other prisms see the rectangular prism calculator, or solve the end triangle on its own with the triangle calculator.
Frequently asked questions
What is the formula for the volume of a triangular prism?
Multiply the area of the triangular end by the length of the prism: V = B × L. With a base of 6 ft, a triangle height of 4 ft and a length of 8 ft, the end area is 12 ft² and the volume is 96 ft³.
Why does the surface area need all three sides of the triangle?
The three rectangular faces have widths equal to the three sides of the triangle, so their areas are a × L, b × L and c × L. Base and height alone fix the triangle's area, and therefore the volume, but not the lengths of the two slanted sides.
Which face is the base of a triangular prism?
In geometry the bases are the two identical triangles at the ends, even if the prism is lying on one of its rectangular faces. The length L is the distance between those triangles.
How do I find the volume of a wedge or ramp?
A wedge with a right-triangle cross-section is a right triangular prism. Choose the two-legs option, enter the rise and run as the legs and the width of the ramp as the length. A ramp rising 1.5 ft over 2 ft and 10 ft wide holds 15 ft³.
Can I enter the angle in radians?
Yes. In the two-sides-and-angle option, an Angle unit menu lets you choose degrees or radians. The other options do not use an angle input.