What Is a Rectangular Prism?
A rectangular prism (also called a cuboid or a box) is a three-dimensional solid with six rectangular faces, where all angles are right angles. Everyday examples include shipping boxes, bricks, aquariums, and rooms. Its size is fully described by three measurements: length (\(l\)), width (\(w\)), and height (\(h\)).
How to Use This Calculator
Enter the length, width, and height of your prism in the same unit of measurement (for example, all in centimeters or all in inches). Press calculate to get the volume in cubic units, along with the total surface area. Because the formula is unit-agnostic, the result simply uses whatever unit you supplied — meters give cubic meters, feet give cubic feet, and so on.
The Formula Explained
The volume of a rectangular prism is found by multiplying its three dimensions together: $$V = \text{Length} \times \text{Width} \times \text{Height}$$ Geometrically, you are stacking the base area (length \(\times\) width) up to the prism's height. The surface area sums the areas of all six faces: $$S = 2\left(\text{Length}\cdot\text{Width} + \text{Length}\cdot\text{Height} + \text{Width}\cdot\text{Height}\right)$$
Worked Example
Suppose a box is 5 units long, 4 units wide, and 3 units tall. The volume is $$5 \times 4 \times 3 = 60 \text{ cubic units}.$$ The surface area is $$2 \times (5\times4 + 5\times3 + 4\times3) = 2 \times (20 + 15 + 12) = 2 \times 47 = 94 \text{ square units}.$$
FAQ
Do all sides have to use the same unit? Yes — mixing units (e.g., length in feet and width in inches) gives a meaningless result. Convert everything to one unit first.
Is a cube a rectangular prism? Yes. A cube is a special case where length, width, and height are all equal, so \(V = s^3\).
Can I use decimals? Absolutely. The calculator accepts any positive decimal value for each dimension.
