Prism & Pyramid Volume Calculator
How It Works
This prism & pyramid volume calculator uses established formulas to provide accurate results.
The basic rule:
- V(rect prism) = l × w × h
- V(pyramid) = ⅓ × base area × height
- V(tri prism) = ½ × b × h × length
- SA(rect prism) = 2(lw + wh + lh)
Results are estimates. Consult a professional for critical decisions.
Frequently Asked Questions
What is the difference between a prism and a pyramid?
A prism has two parallel, congruent bases connected by rectangular faces. A pyramid has one base and triangular faces that meet at a single apex point. Prism volume = base area × height; pyramid volume = ⅓ × base area × height.
How do you find the surface area of a pyramid?
The surface area of a pyramid equals the base area plus the sum of the areas of all triangular faces. For a square pyramid: SA = base² + 2 × base × slant height.
Why is pyramid volume one-third of a prism?
A pyramid's volume is exactly ⅓ of a prism with the same base and height. This can be proven by dividing a cube into three congruent pyramids, each with volume ⅓ of the cube.
What dimensions do I enter for a triangular prism?
Enter the base of the triangle as dim1, the triangle's height as dim2, and the length (depth) of the prism as dim3. The calculator computes the triangular cross-section area first, then multiplies by the prism length.