Cuboid Calculator

Calculate volume, surface area, space diagonal, and other properties of any cuboid instantly

Calculate Using:

Length (l): Width (w): Height (h):

Calculation Results

Enter cuboid measurements to calculate all properties.

Cuboid Diagram

The Cuboid: A Fundamental 3D Shape

A cuboid is a three-dimensional shape with six rectangular faces, where all angles are right angles and opposite faces are equal. It's a generalization of a cube where the sides can have different lengths.

Key Properties of a Cuboid

Length (l) - The longest dimension of the cuboid.
Width (w) - The medium dimension of the cuboid.
Height (h) - The shortest dimension of the cuboid.
Volume (V) - The space contained within the cuboid (l × w × h).
Surface Area (S) - The total area of all faces (2(lw + lh + wh)).
Space Diagonal (d) - The longest diagonal through the cuboid (√(l² + w² + h²)).
Face Areas - Three distinct rectangular face areas (l×w, l×h, w×h).

Mathematical Equations of a Cuboid

Volume: V = l × w × h
Surface Area: S = 2(lw + lh + wh)
Space Diagonal: d = √(l² + w² + h²)
Front Area: A_front = l × h
Side Area: A_side = w × h
Top Area: A_top = l × w

Why Are Cuboids Important?

Architecture & Construction - Most buildings and rooms are cuboid-shaped.
Packaging - Boxes and containers often use cuboid shapes for efficient stacking.
Engineering - Structural components frequently have cuboid forms.
3D Graphics - Cuboids are fundamental bounding volumes in computer graphics.

Facts About Cuboids

A cube is a special cuboid where length = width = height.
The cuboid is one of the most common shapes in everyday life (books, phones, rooms).
The space diagonal is always longer than any face diagonal.

Cuboids are fundamental geometric shapes with practical applications in virtually every field that deals with three-dimensional space.

Length (l)

Height (h)

Width (w)

Volume (V)

Surface Area (S)

Space Diagonal (d)

Cuboid Formulas

Volume: V = l × w × h
Surface Area: S = 2(lw + lh + wh)
Space Diagonal: d = √(l² + w² + h²)
Front Area: A_front = l × h
Side Area: A_side = w × h
Top Area: A_top = l × w

How to Use the Cuboid Calculator

The Cuboid Calculator helps compute various properties based on input values. Here's how to use it:

1 Select What You Know

Choose the known values combination:

Dimensions - Length, width and height
Volume & Two Dimensions
Surface Area & Two Dimensions
Space Diagonal & Two Dimensions
Space Diagonal & One Dimension
Face Areas - Front, side and top areas

2 Enter the Values

Type in positive numeric values for your selected parameters.

Example: l = 5, w = 3, h = 2

3 Click "Calculate"

The calculator will compute:

All dimensions (length, width, height)
Volume
Surface area
Space diagonal
All face areas

Example Use Cases

Calculate the volume of a rectangular box.
Determine the amount of wrapping paper needed for a gift box.
Find the longest rod that can fit inside a rectangular room.

Example Calculations

Example 1: l = 5 units, w = 3 units, h = 2 units
- Volume = 5 × 3 × 2 = 30 units³
- Surface Area = 2(15 + 10 + 6) = 62 units²
- Space Diagonal ≈ 6.16 units
Example 2: V = 60 cm³, w = 4 cm, h = 3 cm
- Length = 5 cm
- Surface Area = 94 cm²
- Space Diagonal ≈ 7.07 cm

Frequently Asked Questions

1. What's the difference between a cuboid and a rectangular prism?

They are essentially the same shape. Cuboid is the more general mathematical term, while rectangular prism is often used in elementary geometry.

2. How do you find the dimensions if you know volume and surface area?

You can set up equations V = lwh and S = 2(lw + lh + wh), then solve the system of equations. There may be multiple valid solutions.

3. Can a cuboid have two equal dimensions?

Yes! When two dimensions are equal (e.g., l = w ≠ h), it's called a "square cuboid". When all three are equal (l = w = h), it becomes a cube.

4. What are real-world examples of cuboids?

Bricks and building blocks
Books and smartphones
Shipping containers
Refrigerators and cabinets