Tents, Toblerone boxes, roof sections, ramps and optical prisms are triangular prisms. Their volume is the triangle’s area times the length.
How to use the Triangular Prism Calculator
- Triangle base given by
- Side a
- Side b
- Side c
- Angle γ (between a and b)
- Angle β (at one end of a)
- Angle γ (at the other end of a)
- Base b
- Height h
- Prism length L
Results update as you type, and everything is calculated in your browser.
How it works
Choose how the triangle is known. Missing sides come from the law of cosines or sines; with base and height, the volume and base area are found but the side lengths (and so the surface area) are not.
Inputs explained
| Field | What to enter |
|---|---|
| Triangle base given by | Choose one: Three sides, Two sides and the angle between them, Two angles and the side between them, Right triangle (two legs) … |
| Side a | Units: cm, m, mm, in, ft, yd … |
| Side b | Units: cm, m, mm, in, ft, yd … |
| Side c | Units: cm, m, mm, in, ft, yd … |
| Angle γ (between a and b) | Units: °, rad, π rad, grad, turn |
| Angle β (at one end of a) | Units: °, rad, π rad, grad, turn |
| Angle γ (at the other end of a) | Units: °, rad, π rad, grad, turn |
| Base b | Units: cm, m, mm, in, ft, yd … |
| Height h | Units: cm, m, mm, in, ft, yd … |
| Prism length L | Units: cm, m, mm, in, ft, yd … |
What each result means
- Volume = [Triangle (base) area]×[Prism length L]
- Lateral area = ([a] + [b] + [c])×[Prism length L]
- Total surface area = 2×[Triangle (base) area] + ([a] + [b] + [c])×[Prism length L]
Example values
How the main result changes when Side a changes and everything else stays at the example values above:
| Side a (cm) | Volume (cm³) |
|---|---|
| 1.5 | 24.8039 |
| 2.25 | 43.9101 |
| 3 | 60 |
| 3.75 | 73.9244 |
| 4.5 | 85.4926 |
| 6 | 99.2157 |
Formula
V = A_base·L, A = 2·A_base + (a + b + c)·L
Worked example
Inputs: Triangle base given by: Three sides; Side a: 3 cm; Side b: 4 cm; Side c: 5 cm; Prism length L: 10 cm.
Results: Triangle (base) area = 6 cm²; Volume = 60 cm³; Lateral area = 120 cm²; Total surface area = 132 cm².
Key terms
- Prism
- A solid with two identical parallel bases joined by parallelograms.
Frequently asked questions
How do I find the volume of a triangular prism?
Triangle area × length.
What if I only know base and height?
That gives the volume, but you need the sides for the surface area.
How many faces does a triangular prism have?
Five: two triangles and three rectangles.
What is a right triangular prism?
One whose lateral faces are perpendicular to the bases.