Volume of a Rectangular Prism Calculator

Welcome to the Volume of a Rectangular Prism Calculator, your comprehensive tool for calculating the volume, surface area, and diagonal of any rectangular prism (also known as a cuboid or rectangular box). Whether you are working on construction projects, packaging design, shipping calculations, or math homework, this calculator provides accurate results with step-by-step explanations and interactive 3D visualization.

What is a Rectangular Prism?

A rectangular prism (also called a cuboid or rectangular box) is a three-dimensional solid shape with six rectangular faces. It has:

• 6 faces - All faces are rectangles, with opposite faces being equal
• 8 vertices - The corners where three edges meet
• 12 edges - Four edges of each dimension (length, width, height)
• 3 dimensions - Length (l), Width (w), and Height (h)

When all three dimensions are equal, the rectangular prism becomes a special case called a cube.

Rectangular Prism Formulas

Volume Formula

The volume represents the amount of space inside the prism, measured in cubic units.

Surface Area Formula

The surface area is the total area of all six faces combined, measured in square units.

Space Diagonal Formula

The space diagonal is the longest line that can be drawn inside the prism, connecting two opposite corners through the interior.

Lateral Surface Area

The lateral surface area includes only the four side faces, excluding the top and bottom.

How to Use This Calculator

1. Enter dimensions: Input the length, width, and height of your rectangular prism. Use the quick example buttons to test with common values.
2. Select unit: Choose your preferred unit of measurement (meters, centimeters, inches, feet, etc.).
3. Set precision: Select the number of decimal places for your results.
4. Calculate: Click the calculate button to see comprehensive results including volume, surface area, diagonal, and more.
5. Review results: Examine the 3D visualization, step-by-step calculations, and unit conversion table.

Real-World Applications

Frequently Asked Questions

What is the formula for the volume of a rectangular prism?

The volume of a rectangular prism is calculated using the formula V = l × w × h, where l is the length, w is the width, and h is the height. Simply multiply all three dimensions together to get the volume in cubic units.

How do you calculate the surface area of a rectangular prism?

The total surface area of a rectangular prism is calculated using SA = 2(lw + lh + wh). This formula accounts for all six faces: two faces of each type (length×width, length×height, and width×height).

What is the difference between a rectangular prism and a cuboid?

A rectangular prism and a cuboid are the same thing - a 3D shape with six rectangular faces, where opposite faces are equal. It is also commonly called a rectangular box. When all sides are equal, it becomes a cube.

How do you find the space diagonal of a rectangular prism?

The space diagonal (the longest diagonal running through the interior from one corner to the opposite corner) is calculated using d = √(l² + w² + h²). This is an extension of the Pythagorean theorem to three dimensions.

Additional Resources

• Cuboid - Wikipedia
• Volume - Wikipedia