# Rectangular Prism Calculator

Calculate volume, surface area, and space diagonal of a rectangular prism. Also shows face diagonals and lateral area. Free box calculator.

## What this calculates

Calculate the volume, surface area, space diagonal, face diagonals, and lateral area of any rectangular prism (box shape). Enter the length, width, and height for instant results.

## Inputs

- **Length** — min 0 — The length of the rectangular prism.
- **Width** — min 0 — The width of the rectangular prism.
- **Height** — min 0 — The height of the rectangular prism.

## Outputs

- **Volume** — The volume of the rectangular prism (length x width x height).
- **Surface Area** — The total surface area of all six faces.
- **Space Diagonal** — The longest diagonal, running from one corner to the opposite corner through the interior.
- **Face Diagonals** — formatted as text — The diagonals of the three different face types.
- **Lateral Surface Area** — The surface area of the four side faces (excludes top and bottom).

## Details

A rectangular prism (also called a rectangular cuboid or simply a box) is a 3D solid with six rectangular faces, all angles being 90 degrees.

**Key Formulas:**

- **Volume:** V = length x width x height
- **Surface Area:** SA = 2(lw + lh + wh)
- **Space Diagonal:** d = sqrt(l² + w² + h²)
- **Lateral Surface Area:** LA = 2h(l + w) (just the four sides, no top or bottom)

**Example:**

A box that is 5 x 3 x 4:
- Volume = 60 cubic units
- Surface Area = 2(15 + 20 + 12) = 94 square units
- Space diagonal = sqrt(25 + 9 + 16) = sqrt(50) = 7.071 units

**Practical Uses:**

- **Shipping:** Volume tells you capacity, surface area tells you how much wrapping or cardboard you need
- **Construction:** Concrete volume for foundations, paint for walls (lateral area)
- **Storage:** Whether an object fits inside a box (check the space diagonal for long items)
- **Aquariums:** Volume determines water capacity; 1 gallon = 231 cubic inches

## Frequently Asked Questions

**Q: What is the difference between a rectangular prism and a cube?**

A: A cube is a special rectangular prism where all three dimensions (length, width, height) are equal. Every cube is a rectangular prism, but not every rectangular prism is a cube. A cube has six square faces, while a general rectangular prism can have rectangular faces of different sizes.

**Q: What is the space diagonal?**

A: The space diagonal is the longest possible straight line inside the box, running from one corner to the opposite corner through the interior. It is calculated as d = sqrt(l² + w² + h²). This is useful for determining whether a long object (like a fishing rod or umbrella) will fit inside a box.

**Q: How do I calculate how much wrapping paper I need?**

A: The surface area gives the minimum amount of wrapping needed. Calculate SA = 2(lw + lh + wh). In practice, you need extra for overlaps, folds, and waste. A good estimate is to add about 15-20% to the calculated surface area.

**Q: How do I convert volume to gallons or liters?**

A: If your dimensions are in inches, divide the volume in cubic inches by 231 to get US gallons, or by 61.024 to get liters. If your dimensions are in centimeters, divide cubic centimeters by 1000 to get liters. A standard milk carton (half gallon) is about 1893 cubic centimeters.

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