Prism Volume Calculator
Calculate the volume of a triangular prism
By Drew Budwin · Last updated July 2026 · Methodology
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Prism Volume Calculator Formula
Volume of a triangular prism:
V = (1/2) × b × a × l
b = triangle base, a = triangle height, l = prism length
How to Use This Calculator
- Enter the base of the triangular cross-section.
- Enter the triangle height (the perpendicular height of the triangle, not the prism length).
- Enter the length of the prism (how far it extends in the third dimension).
- Click Calculate Volume to see the result.
Frequently Asked Questions
What is the difference between triangle height and prism length?
The triangle height (a) is the perpendicular height inside the triangular cross-section, measured from the base to the opposite vertex. The prism length (l) is how far the prism extends in the third dimension, perpendicular to the triangle face.
What if I only know the three sides of the triangle?
Use Heron's formula to find the triangle's area first: A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. Then V = A × l. Or use the triangle area calculator to get A, then multiply by l.
What units does this calculator use?
This calculator is unit-agnostic. If all inputs are in centimeters, the result is in cubic centimeters (cm³). Use the same unit for all inputs.
What everyday objects are triangular prisms?
Common examples include tent shapes, Toblerone chocolate boxes, roof ridges, door wedges, and triangular display stands. The cross-section has to stay the same from end to end, so a bent or tapered shape doesn't count.
What is the surface area of a triangular prism?
The surface area is the sum of the two triangular end faces plus the three rectangular side faces: SA = 2 × (triangle area) + (perimeter of triangle) × length.
How is a triangular prism used in engineering?
Highway cuts through hills often have triangular cross-sections. Calculate the cross-sectional area and multiply by the cut's length to estimate the volume of earth to remove. Roof trusses and structural beams also rely on triangular prism geometry.
Can I use this for an oblique prism?
Yes. Volume = base area × perpendicular height holds for any prism, oblique or right. If the lateral edges tilt, use the perpendicular distance between the base planes as the height — not the slant edge length.
How does a triangular prism compare in volume to a rectangular box with the same footprint?
A triangular prism uses exactly half the space of a rectangular box with the same base b, width a, and length. The triangle cross-section has area (1/2)ba, while the rectangle has area ba. Same footprint, half the volume.