What Is a Rectangular Prism?
A rectangular prism (also called a box or cuboid) is a three-dimensional solid with six rectangular faces, where every angle is a right angle. Its three dimensions—length, width, and height—fully describe its size. This calculator finds the volume (the amount of space inside) and, as a bonus, the total surface area.
How to Use This Calculator
Enter the length, width, and height of your box using any consistent unit (all in centimeters, all in inches, etc.). The result is the volume in cubic units of whatever unit you entered. For example, if you measure in centimeters, the volume is in cubic centimeters (cm³).
The Formula Explained
The volume of a rectangular prism is simply the product of its three dimensions:
$$V = l \times w \times h$$
This works because volume measures how many unit cubes fit inside the box. Multiplying length by width gives the area of the base, and multiplying that area by the height stacks those base layers to fill the solid. The surface area uses $$A = 2(lw + lh + wh)$$, summing the areas of all six faces.
Worked Example
Suppose a box is 5 units long, 4 units wide, and 3 units high. The volume is $$V = 5 \times 4 \times 3 = 60 \text{ cubic units}.$$ The surface area is $$A = 2(5\times4 + 5\times3 + 4\times3) = 2(20 + 15 + 12) = 2 \times 47 = 94 \text{ square units}.$$
FAQ
What units does the answer use? The volume is in cubic units of whatever unit you entered (e.g., cm in → cm³). Always use the same unit for all three dimensions.
Can I use decimals? Yes. Enter any positive decimal value, such as 2.5 or 10.75.
Is a cube a rectangular prism? Yes. A cube is a special case where length, width, and height are all equal, so \(V = s^3\).
