Free Rectangular Prism Calculator

What Is a Rectangular Prism?

A rectangular prism, commonly called a cuboid, is a three-dimensional solid bounded by six rectangular faces. In a right rectangular prism, adjacent faces meet at 90° angles, producing the familiar box shape. This free rectangular prism calculator focuses on the right‑angled version, which is the most common in everyday objects—from shipping containers to bookshelves. A rectangular prism possesses six faces, eight vertices, and twelve edges.

Volume of a Rectangular Prism

The interior capacity of a rectangular prism is computed by multiplying its three perpendicular dimensions:

$$V = l \times w \times h$$

where $l$, $w$, and $h$ denote length, width, and height respectively. The units must be consistent (e.g., all in inches) to obtain the volume in cubic units.

The following table illustrates how different dimension sets produce different volumes, together with the corresponding surface areas and space diagonals.

Length (in)	Width (in)	Height (in)	Volume (in³)	Surface Area (in²)	Diagonal (in)
18	12	15	3240	1332	26.33
10	10	10	1000	600	17.32
24	8	6	1152	768	25.06

Only one dimension is insufficient to determine volume; all three values are required. When the prism is a cube (all sides equal), the formula reduces to $V = s^{3}$, as exemplified by the second row of the table.

Surface Area of a Rectangular Prism

The total area covering the outside of the prism is given by summing the areas of all six faces. Because opposite faces are identical, the expression simplifies to:

$$SA = 2(lw + lh + wh)$$

For the 18 × 12 × 15 in prism (first row of the table), the three unique rectangular areas are:

• top / bottom: $216\;\text{in}^{2}$
• front / back: $270\;\text{in}^{2}$
• left / right: $180\;\text{in}^{2}$

Their total is $666\;\text{in}^{2}$, which doubled gives $1332\;\text{in}^{2}$. The rectangular prism surface area calculator in this tool performs this multiplication instantly.

Diagonal of a Rectangular Prism

The longest straight line between two opposite corners inside the prism is its space diagonal, computed using a three‑dimensional Pythagorean relation:

$$d = \sqrt{l^{2} + w^{2} + h^{2}}$$

Applying this to the same 18 × 12 × 15 prism:

$$d = \sqrt{18^{2} + 12^{2} + 15^{2}} = \sqrt{324 + 144 + 225} = \sqrt{693} \approx 26.33\;\text{in}$$

The tool’s diagonal of a rectangular prism function returns this value without manual square‑root calculations.

Using the Calculator

This free rectangular prism calculator online is designed for immediate, accurate results. You enter the length, width, and height, and it simultaneously reports the cuboid volume, total surface area, and diagonal. Whether you are planning a DIY project, checking packaging specifications, or solving a geometry problem, this volume of a rectangular prism calculator and surface area tool eliminates repetitive arithmetic.