A prism with a triangular cross-section, common in roof trusses, tents, and wedge-shaped structures.
How it works
The triangular cross-section’s area (base times height, divided by 2) is multiplied by the prism’s length to get the total volume.
What this does not include
This does not include other prism shapes — for a trapezoid cross-section, use this site’s trapezoidal prism calculator instead.
How to use this calculator
- Enter the triangle’s base, its height, and the prism length.
A worked example
A triangular prism with triangle base 6, triangle height 4, and prism length 10: volume = (½ × 6 × 4) × 10 = 120.
Base 3, height 4, length 5: volume = 30.
What the variables mean
| Variable | Meaning |
|---|---|
| Base | Base of the triangular cross-section |
| Triangle height | Height of the triangular cross-section |
| Length | How far the triangular cross-section is extruded |
Edge cases worth knowing
This formula only depends on the triangle’s base and height, not its full shape. A very tall thin triangle and a short wide one with the same base × height give identical prism volumes.
A base of zero collapses the cross-section to a line, leaving no volume, so the calculator declines to show a result.
Frequently asked questions
What’s a real-world example of a triangular prism?
A classic tent shape, a roof truss cross-section, or a Toblerone-style wedge — all extend a triangular cross-section along a length.
Is the triangle height the same as the prism length?
No — the triangle height is the cross-section’s own perpendicular height, while the prism length is how far that triangular cross-section extends.
Does this work for any triangle shape?
Yes — as long as the correct perpendicular height for the chosen base is used, this formula works for any triangle cross-section, not just equilateral or right triangles.
