triangular prism volume calculator
Calculate a triangular prism's volume in cubic feet, cubic yards, gallons, and liters from triangle base, triangle height, and prism length.
A triangular prism keeps a constant triangular cross-section along its length — the shape of a gable fill, a ridge pile, or a wedge-shaped footing. Enter the triangle’s base and height plus the prism’s length to get volume in cubic feet, cubic yards, gallons, and liters.
How this calculator works
Triangular prism volume is the triangle’s cross-sectional area times the prism’s length.
Formula: Cubic feet = 0.5 × base × triangle height × prism length. Cubic yards = ft³ ÷ 27. Gallons = ft³ × 7.48052. Liters = ft³ × 28.3168.
Worked example
A triangular prism with a 4 ft base, 3 ft triangle height, and 10 ft length:
- Cubic feet: 0.5 × 4 × 3 × 10 = 60.00 ft³
- Cubic yards: 60 ÷ 27 ≈ 2.222 yd³
- Gallons: 60 × 7.48052 ≈ 448.8 gal
- Liters: 60 × 28.3168 ≈ 1699.0 L
Reference
| Base × Tri height × Length (ft) | Cubic feet |
|---|---|
| 2 × 2 × 8 | 16.00 ft³ |
| 4 × 3 × 10 | 60.00 ft³ |
| 6 × 4 × 12 | 144.00 ft³ |
How to measure
Measure the triangular cross-section’s base and its perpendicular height straight up from that base, then measure the total run length of the prism. This applies to gable-end fill, ridge-shaped piles, and V-shaped trench or wedge footings. For a rectangular cross-section instead, use the Rectangular Prism Volume Calculator.
Frequently asked questions
What's the formula for triangular prism volume?
Volume is the triangle's area times the prism's length: V = 0.5 × base × triangle height × prism length. The 0.5 comes from the standard triangle area formula.
What's the difference between the triangle's base and height, and the prism's length?
The base and height define the flat triangular end — think of the cross-section you'd see cutting straight through the shape. The length is how far that triangular cross-section extends, at a constant size, in the third direction.
Where does a triangular prism shape show up in construction?
A gable end fill, a ridge-shaped material pile, a V-shaped trench or footing cross-section, and A-frame structural forms are all triangular prisms — the triangle stays the same shape along the run.
Is the triangle height the same as the slanted side of the triangle?
No — it's the perpendicular distance from the base to the opposite point, measured straight up, not along a sloped edge. Using the slanted side instead will overstate the volume.
How would I estimate concrete for a ridge-shaped or wedge footing?
Measure the triangular cross-section's base and height, and the total run length of the wedge, enter all three, and the cubic yards result is what you'd order from a ready-mix supplier.
How does this compare to a rectangular prism of similar size?
A triangular prism holds exactly half the volume of a rectangular prism with the same base, height, and length, since the triangle covers half the area of the equivalent rectangle. Check the Rectangular Prism Volume Calculator to compare side by side.
Estimates only. Verify quantities with your supplier before purchasing.