A triangular prism volume calculator that gives you the result in one click — plus optional step-by-step working, a labeled SVG diagram, solve-for-variable (find base, height, or length when volume is known), and an expandable surface area section using Heron’s formula. Everything runs in your browser; no data is sent anywhere.
How it works
A triangular prism is a 3-D solid whose cross-section is a triangle and whose length (depth) is the straight extrusion of that triangle. The volume is simply the cross-sectional area multiplied by the length:
V = A_triangle x L = (1/2) x b x h x L
where b is the base of the triangle, h is the perpendicular height of the triangle (the altitude from the base to the opposite vertex — not a slant side), and L is the prism length. The calculator shows each multiplication step so you can verify the arithmetic at a glance.
The tool also supports solving for a missing dimension. Select “Base (given volume)”
from the dropdown and type the known volume into the Base field; the rearranged formula
b = 2V / (h x L) is applied immediately.
For surface area, the tool uses Heron’s formula to find the triangle’s area from all three side lengths, then adds the three rectangular lateral faces:
SA = 2 x A_triangle + (a + b + c) x L
If you leave side c blank, a right triangle is assumed and the hypotenuse is computed as
sqrt(a squared + b squared).
Worked example
Suppose you are calculating how much concrete to pour into a triangular-prism-shaped mould:
- Triangle base (b) = 6 cm
- Triangle height (h) = 4 cm
- Prism length (L) = 10 cm
Step 1 — triangle area: A = (1/2) x 6 x 4 = 12 cm squared
Step 2 — prism volume: V = 12 x 10 = 120 cm cubed
Now suppose you know the volume must be 180 cm cubed but the base is unknown. Keep
h = 4 and L = 10, select “Base (given volume)” and enter 180. The result:
b = (2 x 180) / (4 x 10) = 360 / 40 = 9 cm.
| b (cm) | h (cm) | L (cm) | Volume (cm cubed) |
|---|---|---|---|
| 6 | 4 | 10 | 120 |
| 3 | 5 | 8 | 60 |
| 12 | 7 | 15 | 630 |
| 10 | 10 | 20 | 1,000 |
Formula reference
The key relationships, rearranged for each unknown:
- Volume:
V = (1/2) x b x h x L - Base:
b = (2 x V) / (h x L) - Triangle height:
h = (2 x V) / (b x L) - Prism length:
L = (2 x V) / (b x h)
Surface area (any triangle via Heron’s formula — s = semi-perimeter = (a+b+c)/2):
- Triangle area:
A = sqrt(s(s-a)(s-b)(s-c)) - Total surface area:
SA = 2A + (a + b + c) x L
All formulas are computed to full floating-point precision inside the browser. No rounding occurs until the final display.