# Volume of a Prism Calculator

Calculate the volume and surface area of triangular, rectangular, and hexagonal prisms. Enter dimensions and get instant results.

## What this calculates

Find the volume, base area, lateral surface area, and total surface area of common prisms. Select the base shape, enter your dimensions, and get instant calculations.

## Inputs

- **Base Shape** — options: Triangular Prism, Rectangular Prism, Hexagonal Prism — Select the shape of the prism's base.
- **Base Side / Length** — min 0 — Side length for triangle/hexagon, or length for rectangle.
- **Base Width / Height** — min 0 — Height of triangular base, or width of rectangular base.
- **Prism Length (depth)** — min 0 — The length (depth) of the prism, i.e. the distance between the two bases.

## Outputs

- **Volume** — The volume of the prism: base area × length.
- **Base Area** — The area of one base face.
- **Lateral Surface Area** — The combined area of all side faces (excluding the two bases).
- **Total Surface Area** — The total area of all faces including both bases.

## Details

A prism is a 3D shape with two identical parallel bases connected by rectangular faces. The volume of any prism is simply the base area multiplied by the length (or depth) between the two bases: V = base area × length.

For a rectangular prism (box), the base area is length × width, giving V = l × w × h. For a triangular prism, the base area is (1/2) × base × height of the triangle, so V = (1/2) × b × h_triangle × length. For a regular hexagonal prism, the base is a regular hexagon with area (3√3/2) × s².

The lateral surface area is the sum of all the rectangular side faces, which equals the perimeter of the base multiplied by the prism length. The total surface area adds the two base faces. Prisms are common in architecture (beams, columns), packaging (boxes, Toblerone), and crystallography.

## Frequently Asked Questions

**Q: What is the volume formula for a prism?**

A: The volume of any prism is V = base area × length, where the base area depends on the shape of the base and the length is the distance between the two parallel bases.

**Q: How is a prism different from a pyramid?**

A: A prism has two identical parallel bases connected by rectangular faces, while a pyramid has one base and triangular faces that converge to a single apex. A prism's volume is base area × height; a pyramid's is (1/3) × base area × height.

**Q: What is lateral surface area?**

A: Lateral surface area is the combined area of all the side faces of a prism, excluding the two bases. For a prism, it equals the perimeter of the base multiplied by the length of the prism.

**Q: What is the area of a regular hexagonal base?**

A: A regular hexagon with side length s has area (3√3/2) × s², which is approximately 2.598 × s². It can be divided into 6 equilateral triangles, each with area (√3/4) × s².

---

Source: https://vastcalc.com/calculators/math/volume-of-prism
Category: Math
Last updated: 2026-04-21