What this calculator does
A triangular prism is a solid with a triangular cross-section that stays the same all the way along its length, like a tent, a wedge doorstop or a length of angled roofing. The volume of a triangular prism is the area of that triangular base multiplied by the length, the same principle as any prism: base area times how far it extends.
The base area itself is worked out from the three side lengths using Heron's formula, rather than needing a separate base-and-height measurement, so this calculator only needs the three sides of the triangle and the length of the prism to return both the volume and the total surface area.
The formula
First find the semiperimeter s of the triangular base: (a+b+c)/2. Heron's formula then gives the base area as √(s(s−a)(s−b)(s−c)). Volume is that area multiplied by the prism length. Total surface area adds the two triangular ends (2 × base area) to the three rectangular side faces, whose combined area is the base's perimeter multiplied by the length.
| Term | Meaning |
|---|---|
| Base area | The area of the triangular cross-section, constant along the whole length of the prism. |
| Prism length | The distance the triangular cross-section is extended to form the solid. |
| Semiperimeter | Half the perimeter of the triangular base, used inside Heron's formula. |
The inputs explained
| Field | What to enter |
|---|---|
| Base side a | One side of the triangular base. |
| Base side b | A second side of the triangular base. |
| Base side c | The third side of the triangular base. |
| Prism length | The length the triangular cross-section is extended along to form the prism. |
When to use it
Estimating triangular prism volume for a wedge or ramp
A doorstop, roof wedge or drainage channel with a constant triangular cross-section is exactly this shape, and its capacity or material volume follows directly from the base sides and the length.
Working a textbook triangular prism volume problem
Given the three sides of the base and the prism length, this replaces the two-step process of finding the base area by hand before multiplying by length.
Checking how much material a triangular beam or strut needs
The total surface area figure covers how much material would be needed to wrap or coat every face of the solid, not just its interior volume.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does volume change as a triangular prism gets longer?
A fixed triangular base, extended to a range of lengths.
| Prism length | Volume | Total surface area |
|---|---|---|
| 5 | 26.663 | 75.665 |
| 10 | 53.327 | 140.665 |
| 15 | 79.990 | 205.665 |
| 20 | 106.654 | 270.665 |
| 30 | 159.980 | 400.665 |
| 50 | 266.634 | 660.665 |
How does the base shape affect volume at a fixed length?
The third side of the triangular base varying between the two limits a valid triangle allows.
| Side c | Triangular cross-section area | Volume |
|---|---|---|
| 2 | 2.905 | 29.047 |
| 3 | 4.472 | 44.721 |
| 4 | 5.562 | 55.621 |
| 5 | 6.000 | 60.000 |
| 6 | 5.333 | 53.327 |
| 6.9 | 2.012 | 20.123 |
Questions
What is the formula for the volume of a triangular prism?
Volume equals the area of the triangular base multiplied by the length of the prism. The base area itself comes from Heron's formula once the three side lengths are known, so no separate height measurement is required.
How is a triangular prism's volume different from a rectangular prism's?
A rectangular prism's cross-section is a rectangle, so its volume is length × width × height. A triangular prism swaps that rectangular cross-section for a triangular one, so the base area comes from the triangle's three sides instead of two rectangle dimensions.
Do I need the height of the triangle as well as its sides?
No. Heron's formula finds the triangular base's area directly from its three side lengths, without needing a separate height measurement, so entering the three sides is enough.
Why does the calculator reject some combinations of sides?
The three base sides have to satisfy the triangle inequality, each pair longer than the third, or they cannot form a real triangle at all, which means there is no base area or volume to compute.
For the area of the triangular cross-section on its own, see the triangle from three sides calculator. For a rectangular-based solid instead of a triangular one, see the rectangular prism and cube calculator.