triangular prism volume calculator
A triangular prism volume calculator uses V = ½ × base × triangle height × length: a 4 × 3 ft triangle run 10 ft long holds 60 ft³, or 2.22 yd³.
Triangular prism volume calculator: area of the end times the length
A triangular prism volume calculator finds the area of the triangle at the end of the shape, then stretches it along the length. The formula is V = ½ × base × triangle height × length. A prism with a 4 ft base, a 3 ft triangle height, and a 10 ft length holds 60 cubic feet, which is 2.22 cubic yards, or about 448.8 US gallons.
Think of it as a tent: a triangle at the front and back, with the same shape all the way through.
The formula in plain words
Slice a loaf of bread that is shaped like a long wedge. Every slice is the same triangle. The volume is the area of one slice times the number of feet of loaf.
- Triangle area = ½ × base × triangle height
- Cubic feet = triangle area × length
- Cubic yards = cubic feet ÷ 27
- Gallons = cubic feet × 7.48052
- Liters = gallons × 3.78541
All three measurements go in feet.
Worked examples
- Gable fill, 4 ft base, 3 ft tall, 10 ft long
- Triangle area: ½ × 4 × 3 = 6 ft²
- Cubic feet: 6 × 10 = 60 ft³
- Cubic yards: 60 ÷ 27 = 2.222 yd³
- Gallons: 448.8 gal
- Liters: 1,699.0 L
- V-shaped trench, 3 ft wide at the top, 2 ft deep, 40 ft long
- Triangle area: ½ × 3 × 2 = 3 ft²
- Cubic feet: 3 × 40 = 120 ft³
- Cubic yards: 4.444 yd³
- Gallons: 897.7 gal
In example 2, the “base” is the trench opening at the top and the “triangle height” is the depth, with the point of the V at the bottom. A trench with a flat bottom is a trapezoid, so use the trench volume calculator.
Volume by size
| Base × triangle height × length (ft) | Cubic feet | Cubic yards |
|---|---|---|
| 2 × 2 × 8 | 16.0 | 0.593 |
| 4 × 3 × 10 | 60.0 | 2.222 |
| 3 × 2 × 40 | 120.0 | 4.444 |
| 6 × 4 × 12 | 144.0 | 5.333 |
Triangle versus rectangle
The same footprint as a rectangular prism gives exactly twice the volume. If a 4 × 3 ft rectangle runs 10 ft, it holds 120 ft³. Cut it diagonally and you get two triangular prisms, each 60 ft³.
That is a handy check. Work the rectangular version in your head and halve it.
How to measure
- Base: Lay a tape along the flat side of the triangle, from corner to corner.
- Triangle height: Hold a level or plumb line from the peak straight down to the base. This is not the sloped edge.
- Length: Measure the full run in the third direction.
- Uneven triangles: If the peak is off-center, the formula still works, because only base and height matter.
- Units: Convert inches to feet before you enter.
Common mistakes
- Using the slant side. The height must be perpendicular to the base.
- Forgetting the ½. Without it the answer doubles.
- Mixing up which side is the base. Choose any side as the base, but the height must be measured perpendicular to that side.
- Treating a wedge pile as perfectly triangular. Rounded ends and slumped sides make real piles smaller.
- Using it for a flat-bottomed trench. That cross-section is a trapezoid.
From cubic feet to concrete weight
The 60 ft³ wedge from example 1 is 2.22 yd³ of concrete if you pour it solid. At the 150 lb per ft³ used on this site, that is 60 × 150 = 9,000 lb.
A wedge footing or ridge slab can be heavy before it carries any load. Make sure the ground, forms, and any pump or wheelbarrow route can handle several thousand pounds.
Related calculators
To compare against a box shape, use the rectangular prism volume calculator. For a pointed shape that narrows in both directions, use the pyramid volume calculator, and for a generic box the 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. A 4 ft base, 3 ft triangle height, and 10 ft length give 60 ft³.
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, the cross-section you would see if you cut straight through the shape. The length is how far that triangle 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 windrow), a V-shaped trench or footing cross-section, and A-frame 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 is 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, plus the total run of the wedge. Enter all three and the cubic yards result is what you would order from a ready-mix supplier. Add a margin for waste, and note that small orders can carry minimum charges.
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. Compare with the Rectangular Prism Volume Calculator.
Estimates only. Verify quantities with your supplier before purchasing.