# Surface Area of a Rectangular Prism Calculator

Calculate the total and lateral surface area of a rectangular prism from length, width, and height. Also find volume and space diagonal. Free box surface area calculator.

## What this calculates

Calculate the total surface area, lateral surface area, base area, volume, and space diagonal of a rectangular prism (box). Just enter the length, width, and height to get instant results.

## Inputs

- **Length (l)** — min 0 — The length of the rectangular prism.
- **Width (w)** — min 0 — The width of the rectangular prism.
- **Height (h)** — min 0 — The height of the rectangular prism.

## Outputs

- **Total Surface Area** — The total area of all six faces: 2(lw + lh + wh).
- **Lateral Surface Area** — The area of the four side faces: 2h(l + w).
- **Base Area** — The area of one base (top or bottom): l x w.
- **Volume** — The volume of the rectangular prism: l x w x h.
- **Space Diagonal** — The diagonal from one corner to the opposite: sqrt(l² + w² + h²).

## Details

A rectangular prism (also called a cuboid or box) has six rectangular faces. The total surface area is the sum of the areas of all six faces.

**Total Surface Area Formula:**

SA = 2(lw + lh + wh)

This accounts for three pairs of identical faces: top/bottom (l x w), front/back (l x h), and left/right (w x h).

**Lateral Surface Area:**

The lateral surface area includes only the four side faces, excluding the top and bottom: LSA = 2h(l + w). This is useful when calculating how much material you need to wrap the sides of a box.

**Space Diagonal:**

The space diagonal runs from one corner of the box to the opposite corner, passing through the interior. It equals sqrt(l² + w² + h²). This extends the Pythagorean theorem to three dimensions.

**Practical Applications:**

Knowing the surface area of a box helps you figure out how much wrapping paper, paint, or material you need. Shipping companies use surface area and volume together to determine packaging costs.

## Frequently Asked Questions

**Q: What is the formula for the surface area of a rectangular prism?**

A: The total surface area is SA = 2(lw + lh + wh), where l is length, w is width, and h is height. This formula adds the areas of all three pairs of opposite faces: two bases (l x w), two fronts (l x h), and two sides (w x h).

**Q: What is the difference between total and lateral surface area?**

A: Total surface area includes all six faces of the box. Lateral surface area includes only the four side faces, excluding the top and bottom. The lateral surface area formula is LSA = 2h(l + w). To get total from lateral, add 2 x l x w for the two bases.

**Q: How is a rectangular prism different from a cube?**

A: A cube is a special rectangular prism where all three dimensions (length, width, height) are equal. A cube has surface area = 6s² where s is the side length. A rectangular prism allows all three dimensions to be different.

**Q: What is the space diagonal and how do I calculate it?**

A: The space diagonal is the longest distance inside a rectangular prism, running from one corner to the opposite corner through the interior. It equals sqrt(l² + w² + h²). This is a 3D extension of the Pythagorean theorem.

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Source: https://vastcalc.com/calculators/math/surface-area-rectangular-prism
Category: Math
Last updated: 2026-04-08