Prism Calculator
Calculate the volume, surface area, and space diagonal of a rectangular prism (box) — or any right prism from base area and length.
Everyday Uses
Beams and profiles
Any constant cross-section solid is a prism — compute material volume from area × length.
Pool volume
A pool with a constant cross-section is a prism — get liters for chemicals and heating.
Custom containers
Hexagonal planters, triangular ducts — volume from any base area and length.
Geometry homework
The general prism formula, applied cleanly to any base shape.
Frequently Asked Questions
How do you calculate the volume of a prism?
V = base area × length (or height) — this works for every right prism regardless of the base shape, because the cross-section is constant. For a rectangular prism (box), that simplifies to V = l × w × h.
How do you find the surface area of a rectangular prism?
SA = 2(lw + lh + wh) — two faces of each of the three pairs. An 8 × 5 × 3 box has SA = 2(40 + 24 + 15) = 158 square units. For a general right prism: SA = 2 × base area + base perimeter × length.
What is the space diagonal of a box?
The longest straight line inside a rectangular prism, from one corner to the opposite corner: d = √(l² + w² + h²) — a 3D extension of the Pythagorean theorem. An 8 × 5 × 3 box has d = √(64 + 25 + 9) = √98 ≈ 9.9.
What counts as a prism?
A prism is a solid with two identical, parallel polygon bases connected by rectangular (in a right prism) faces. Prisms are named by their base: triangular, rectangular, pentagonal, hexagonal. Cylinders follow the same volume rule (base area × height) but are not prisms because their base is a circle, not a polygon.