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Rectangular Prism Volume Calculator

Get rectangular prism volume, surface area & diagonal

Privacy: your files never leave your device. All processing happens locally in your browser.

How to use

  1. 1.Enter the length (l) of the rectangular prism, for example 2.
  2. 2.Enter the width (w) and height (h), for example 3 and 4.
  3. 3.Read the volume (l × w × h = 24), surface area and space diagonal as they update instantly.

About Rectangular Prism Volume Calculator

A rectangular prism — also called a cuboid or, more casually, a box — is a solid with six flat rectangular faces meeting at right angles. Every shoebox, brick, fish tank, shipping carton and room is a rectangular prism, which is why its volume is one of the most useful measurements in everyday geometry. This rectangular prism volume calculator takes the three dimensions you type — length, width and height — and instantly returns the volume, the surface area and the space diagonal, all computed privately in your browser.

The volume of a rectangular prism is length × width × height, written V = l · w · h. The logic is simple: the base is a rectangle of area l × w, and the height h stacks that base upward, so multiplying the three edges gives the space enclosed. For a box measuring 2 × 3 × 4, the volume is 2 × 3 × 4 = 24 cubic units. Whatever unit you use for the sides, the volume comes out in the cube of that unit: centimetres give cubic centimetres (cm³), inches give cubic inches, metres give cubic metres.

The surface area is the total area of all six faces: S = 2(lw + lh + wh). Because the faces come in three matching pairs, you add the three distinct rectangle areas and double the result. For the same 2 × 3 × 4 box that is 2(6 + 8 + 12) = 52 square units. Surface area is what you need for wrapping, painting or working out how much material a container takes.

The space diagonal is the straight line from one corner of the box to the opposite corner, passing through the interior. It follows from the 3D Pythagorean theorem: d = √(l² + w² + h²). For a 3 × 4 × 12 box the diagonal is √(9 + 16 + 144) = √169 = 13, the longest straight object that could fit inside.

A cube is simply the special case where length, width and height are all equal. When l = w = h = s, the formulas collapse to the familiar V = s³, S = 6s², and diagonal = s√3, and this calculator flags that case automatically.

Where does this get used? Volume tells you the capacity of a water tank or aquarium in litres, the amount of concrete for a footing, or the volume of a room for heating and ventilation. Shipping and logistics rely on it for dimensional (volumetric) weight, where carriers bill by the box's volume rather than its actual mass. Students use it for homework and exam practice, and DIY builders use it to estimate materials.

To use the tool, enter the length, then the width and height, and read the volume, surface area and diagonal as they update in real time. Lengths can be whole numbers or decimals, they must be zero or positive, and everything runs locally with nothing uploaded to a server.

Frequently asked questions

How do I calculate the volume of a rectangular prism?
Multiply the three dimensions together: volume = length × width × height (V = l · w · h). For a box that is 2 by 3 by 4, the volume is 2 × 3 × 4 = 24 cubic units. The result is always in cubic units of whatever unit you used for the sides — centimetres give cm³, inches give cubic inches.
What is the l x w x h formula?
l x w x h is shorthand for length times width times height, the formula for the volume of a rectangular prism (cuboid). The base rectangle has area l × w, and multiplying by the height h stacks that base to fill the box. So a 10 × 2 × 3 box holds 10 × 2 × 3 = 60 cubic units.
How do I find the surface area of a rectangular prism?
Add the areas of the three distinct faces and double the total: surface area = 2(lw + lh + wh). The six faces form three matching pairs, which is where the factor of 2 comes from. For a 2 × 3 × 4 box that is 2(6 + 8 + 12) = 52 square units.
What is a cuboid, and how is it different from a cube?
A cuboid is another name for a rectangular prism — a box with six rectangular faces and right-angle corners, where the length, width and height can all differ. A cube is the special case where all three sides are equal (l = w = h), so its volume simplifies to s³ and its surface area to 6s².
How do I find the space diagonal of a rectangular prism?
Use the 3D Pythagorean theorem: the space diagonal = √(l² + w² + h²). It measures the longest straight line inside the box, corner to opposite corner. For a 3 × 4 × 12 box the diagonal is √(9 + 16 + 144) = √169 = 13 units.

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