Rectangular Prism Volume Calculator
Find the volume, surface area and diagonal of a box.
Results update as you type.
How it works
A rectangular prism, also called a cuboid or box, is a solid with six rectangular faces, and this calculator finds its volume, surface area, and space diagonal from the length, width, and height. You enter the three dimensions, and it returns all three quantities at once. The volume, the space inside, is simply the product of the three edge lengths, telling you how much the box holds. The surface area, the total area of all six faces, is twice the sum of the three distinct face areas, and it matters when you need to know how much material wraps or paints the box. The space diagonal is the longest straight line that fits inside, running from one corner to the opposite corner through the interior, and it comes from applying the Pythagorean theorem in three dimensions. These calculations are everywhere in daily life and work: sizing shipping boxes and storage, estimating paint or wrapping, checking whether an object fits diagonally inside a container, and countless engineering and packaging tasks. Keep all three dimensions in the same unit, and the volume will be in cubic units, the surface area in square units, and the diagonal in the same linear unit. Enter length, width, and height to compute all three.
Volume = l·w·h
The volume of a rectangular prism is the product of its length, width, and height. Its total surface area is twice the sum of the three pairs of faces, length times width plus length times height plus width times height. The space diagonal, the longest straight line inside the box, is the square root of the sum of the squares of the three dimensions.
Source:Solid geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter length, width and height.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Volume updates instantly as you type — no button to press.
Frequently asked questions
How do you find the volume of a rectangular prism?
Multiply the length by the width by the height. For a box measuring two by three by four, the volume is 24 cubic units. This gives the total space inside the prism. Keep all three dimensions in the same unit so the answer comes out in the corresponding cubic unit, which the calculator handles for you.
What is the surface area of a box?
The surface area is the combined area of all six faces, equal to twice the sum of length times width, length times height, and width times height. For a two-by-three-by-four box it is 52 square units. Surface area tells you how much material is needed to cover, wrap, or paint the outside of the box.
What is the space diagonal?
The space diagonal is the longest straight line inside the box, running corner to corner through its interior. It equals the square root of the sum of the squares of the length, width, and height, an application of the Pythagorean theorem in three dimensions. It tells you the longest object that could fit diagonally inside the box.
What is the difference between a prism and a cube?
A cube is a special rectangular prism in which all three dimensions are equal, so every face is a square. A general rectangular prism allows the length, width, and height to differ. This calculator handles any rectangular prism; for a cube, simply enter the same value for all three dimensions.
How is this useful for shipping?
Shipping and storage rely on box volume to gauge capacity and on surface area to estimate packaging material. The space diagonal helps check whether a long item will fit inside a container at an angle. Together these figures let you plan packing, compare box sizes, and calculate dimensional weight used by many carriers.