What this calculator does
A triangular prism is a 3D shape with a triangular cross-section extended along its length, like a tent shape or a wedge. This calculator covers the common right-triangle case: given the two legs that meet at the right angle and how far the shape extends, it works out both the total surface area (all five faces) and the volume.
The surface area is made up of two identical triangular end faces plus three rectangular side faces, one running along each side of the triangle. Since the triangle is a right triangle, its hypotenuse is found from the two legs using the Pythagorean theorem before the third rectangular face's area can be calculated.
The formula
The triangular cross-section area is half the product of the two legs. Volume is that area multiplied by the prism's length. Surface area is twice the triangle area (for the two end faces) plus the triangle's perimeter multiplied by the prism length (for the three rectangular side faces), where the perimeter includes the hypotenuse found via a² + b² = c².
| Term | Meaning |
|---|---|
| Leg | One of the two sides of the right triangle that meet at the right angle. |
| Hypotenuse | The longest side of the right triangle, opposite the right angle, calculated from the two legs. |
| Prism length | How far the triangular cross-section is extended to form the 3D prism. |
The inputs explained
| Field | What to enter |
|---|---|
| Right-triangle leg a (m) | The length of one leg of the right-triangle cross-section. |
| Right-triangle leg b (m) | The length of the other leg of the right-triangle cross-section. |
| Prism length (m) | How far the prism extends along its length. |
When to use it
Estimating material for a wedge-shaped structure
A ramp, doorstop or roof-truss end piece with a right-triangle cross-section needs both its volume (for material quantity) and its surface area (for a covering or coating) calculated.
A classroom geometry problem
Triangular prisms with right-triangle cross-sections are a common textbook shape for practising both surface area and volume calculations together.
Checking a 3D-printing or CAD model
Confirming the expected surface area and volume of a simple prism shape is a quick sanity check before committing to a print or fabrication job.
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 do surface area and volume scale with prism length, for a fixed 3-4-5 triangle?
The classic 3-4-5 right-triangle cross-section, extended to different prism lengths.
| Prism length | Surface area | Volume |
|---|---|---|
| 1 m | 24.000 m² | 6.000 m³ |
| 5 m | 72.000 m² | 30.000 m³ |
| 10 m | 132.000 m² | 60.000 m³ |
| 20 m | 252.000 m² | 120.000 m³ |
| 50 m | 612.000 m² | 300.000 m³ |
Questions
Does this work for a triangle that isn't a right triangle?
No, this calculator is scoped to a right-triangle cross-section specifically, since that lets the hypotenuse be found directly from the two legs. A general (non-right) triangular prism needs all three side lengths given directly rather than derived from two legs.
Why are there five faces on a triangular prism?
Two identical triangular end faces, plus one rectangular face running along each of the triangle's three sides, giving five faces in total.
How is the hypotenuse calculated?
Using the Pythagorean theorem: the hypotenuse equals the square root of (leg a squared plus leg b squared), the standard relationship for any right triangle.
What units should I use?
Any consistent length unit works, since the formulas are unit-independent; just make sure both legs and the prism length are entered in the same unit, and read the area result in that unit squared and the volume result in that unit cubed.
For the hypotenuse calculation alone, see the hypotenuse calculator. For a general triangle's area from its side lengths, see the triangle area calculator.