Cuboid
Free cuboid calculator -- compute volume, surface area, and space diagonal from length, width, and height. Ideal for students, architects, and DIY projects.
About This Calculator
The Cuboid Calculator is a versatile tool designed for anyone who needs to compute three fundamental properties of a rectangular box: volume, surface area, and space diagonal. Whether you are a student learning 3D geometry, an architect planning a room, an engineer calculating material requirements, or a DIY enthusiast estimating paint or concrete, this calculator delivers instant, accurate results.
Simply enter the length, width, and height in any consistent unit (meters, centimeters, inches, feet, etc.) and click Calculate. The tool uses standard geometric formulas: Volume = l x w x h, Surface Area = 2(lw + lh + wh), and Space Diagonal = sqrt(l^2 + w^2 + h^2). The same unit system applies to all inputs -- the results adapt automatically: volume in cubic units, surface area in square units, and diagonal in linear units.
The calculator includes two interactive chart modes. The Comparison bar chart displays the three computed values side by side for quick visual comparison. The Composition doughnut chart breaks down the total surface area into its three face-pair contributions (lengthxwidth, lengthxheight, widthxheight), each counted twice for the six faces.
Cuboids are everywhere in the real world: from shipping boxes and suitcases to bricks, books, rooms, and swimming pools. Understanding volume helps with storage capacity, surface area helps with material coverage (paint, wrapping, insulation), and the space diagonal helps determine whether an object will fit through a door or inside another container.
This calculator is fully responsive, works offline after first load, and supports shareable permalinks -- bookmark or share the URL with your dimensions pre-filled.
Frequently Asked Questions
What is a cuboid?
A cuboid is a three-dimensional geometric shape with six rectangular faces, twelve edges, and eight vertices. Opposite faces are equal and parallel. A cube is a special case where all faces are squares of equal side length.
How do you calculate the volume of a cuboid?
The volume of a cuboid is calculated by multiplying its length, width, and height: V = l x w x h. The result is expressed in cubic units (e.g., cm^3, m^3, in^3, ft^3).
How do you calculate the surface area of a cuboid?
The surface area of a cuboid is the sum of the areas of all six faces. The formula is SA = 2(lw + lh + wh), where l is length, w is width, and h is height. The result is expressed in square units.
What is the formula for the space diagonal of a cuboid?
The space diagonal of a cuboid is the longest line segment connecting two opposite vertices through the interior. The formula is d = sqrt(l^2 + w^2 + h^2), derived from applying the Pythagorean theorem twice.
What is the difference between a cube and a cuboid?
A cube is a special type of cuboid where all three dimensions (length, width, height) are equal. While a cuboid can have any rectangular faces, a cube has six identical square faces. All cubes are cuboids, but not all cuboids are cubes.
What units should I use for the measurements?
You can use any consistent unit of length (meters, centimeters, inches, feet, yards, etc.). All three inputs must use the same unit. Volume will be in cubic units and surface area in square units of whatever unit you choose.
What are real-world applications of cuboid calculations?
Cuboid calculations are used everywhere: determining room volume for HVAC sizing (India/UK: cubic meters, US: cubic feet), calculating shipping container capacity, estimating concrete or paint needed for construction projects, designing packaging, and computing water tank storage capacity.