Rectangular Prism Calculator - Volume, Area, Diagonal
Calculate the volume, surface area, space diagonal, and face diagonals of a rectangular prism from its length, width, and height.
Enter the three dimensions of a cuboid to get all major measurements in one result card.
Rectangular Prism Calculator - Volume, Area, Diagonal
Calculate the volume, surface area, space diagonal, and face diagonals of a rectangular prism from its length, width, and height.
About the rectangular prism calculator
A rectangular prism, also called a cuboid, is a three-dimensional solid with six rectangular faces, twelve edges, and eight vertices. Everyday examples include shipping boxes, books, rooms, storage containers, and many building components. Because the shape is so common, its measurements show up constantly in geometry classes, architecture, engineering, manufacturing, packaging, and construction planning.
The most familiar measurement is volume. For a rectangular prism, volume is found by multiplying the three perpendicular dimensions: length × width × height. This tells you how much three-dimensional space the prism occupies. If the dimensions are measured in meters, the volume is measured in cubic meters. Volume matters when you need to know capacity, storage space, material fill, or shipping size.
Surface area is the total area of all six faces. The formula 2(lw + lh + wh) adds the areas of the three distinct face pairs and doubles them because each face type appears twice. Surface area is important when estimating paint, wrapping material, insulation, sheet metal, or any covering needed for the outside of a box-shaped object.
A rectangular prism also has several diagonals. The space diagonal runs from one vertex to the opposite vertex through the interior of the solid. Its length is √(l² + w² + h²), which is a direct extension of the Pythagorean theorem into three dimensions. Each rectangular face has its own diagonal as well: √(l² + w²), √(l² + h²), and √(w² + h²). These face diagonals are useful when checking bracing distances, screen sizes, panel cuts, and diagonal supports on individual faces.
This rectangular prism calculator combines all of those measurements in one place. Enter the length, width, and height, and the tool instantly reports the volume, surface area, space diagonal, and all three face diagonals. That makes it useful for students checking homework, teachers preparing examples, engineers reviewing dimensions, or anyone comparing box-like shapes quickly and accurately.
Rectangular prism examples
These examples show how the same three dimensions produce multiple useful measurements.
| Input | Result | Explanation |
|---|---|---|
| l = 2, w = 3, h = 4 | V = 24, SA = 52, d ≈ 5.3852 | A basic 2 × 3 × 4 prism has volume 24, surface area 52, and a space diagonal of √29. |
| l = 5, w = 5, h = 5 | V = 125, SA = 150, d ≈ 8.6603 | When all three dimensions match, the rectangular prism is a cube. The formulas still apply directly. |
| l = 10, w = 6, h = 2 | V = 120, SA = 184, d ≈ 11.8322 | A long, shallow box can still have a large diagonal because the length contributes heavily to d = √(l² + w² + h²). |
How to use the rectangular prism calculator
- Enter the prism's length, width, and height as positive numbers.
- Click Calculate to compute volume, total surface area, the space diagonal, and all three face diagonals.
- Review the result card to compare the measurements you need for geometry, design, or construction work.
- Use Reset to clear the dimensions and start a new rectangular prism.
Rectangular prism calculator FAQ
What is the difference between volume and surface area?
Volume measures the space inside the prism, while surface area measures the total area covering the outside faces. They answer different physical questions.
What is a space diagonal?
The space diagonal is the line segment connecting one vertex of the prism to the opposite vertex through the interior. Its length is √(l² + w² + h²).
Why are there three face diagonals?
A rectangular prism has three distinct face types: length-width, length-height, and width-height. Each face type has its own diagonal based on the Pythagorean theorem.
Can a cube use this calculator?
Yes. A cube is a special rectangular prism where length, width, and height are equal, so the same formulas apply.
What units does the calculator use?
It uses whatever unit you input consistently. If length, width, and height are in centimeters, then volume is in cubic centimeters, surface area is in square centimeters, and diagonals are in centimeters.