Universal Prism Volume Calculator | Pro Tool
Calculate the volume of any right or oblique prism and the surface area of a right prism, with instant results and step-by-step geometric proofs.
Prism Dimensions
Total 3D capacity
Assumes a right prism
Calculation Logic Live
What is a Prism?
In geometry, a prism is a three-dimensional solid object with two identical ends (called bases) and flat sides (called lateral faces). The key characteristic of any prism is that it maintains the same cross-section along its entire length.
- Two Identical Bases: Parallel polygons (triangles, rectangles, hexagons, etc.).
- Lateral Faces: Parallelograms (usually rectangles in right prisms) connecting the corresponding sides of the two bases.
- Uniform Cross-section: If you slice it anywhere parallel to the base, the shape is identical.
Volume Formulas for All Prism Types
The general formula for any prism is V = Base Area × Height. However, the specific calculation depends on the base shape.
| Prism Type | Formula | Variables |
|---|---|---|
| Rectangular | V = l × w × h | l=length, w=width, h=prism height |
| Triangular | V = ½(b × h_tri) × L | b=base, h_tri=triangle height, L=length |
| Hexagonal | V = (3√3)/2 × s² × h | s=side length, h=height |
Frequently Asked Questions
What is the difference between a prism and a pyramid?
A prism has two identical parallel bases and maintains its thickness throughout. A pyramid has only one base and tapers to a single point (called the apex).
Does this calculator work for oblique prisms?
For volume, yes. According to Cavalieri's Principle, the volume of an oblique (slanted) prism is calculated exactly the same way as a right prism: Base Area multiplied by the perpendicular Height. Surface area is different. The calculator works it out as 2 × Base Area + Perimeter × Height, which is exact for a right prism only: an oblique prism's side faces are parallelograms, and together they are larger than those rectangles, by an amount that depends on how far and in which direction the prism leans — which the calculator does not ask for. For an oblique prism, read the surface area as a lower limit.