Rectangular Prism Calculator
Calculate the volume, surface area, space diagonal, face diagonals, and lateral area of any rectangular prism (box shape). Enter the length, width, and height for instant results.
A rectangular prism (also called a rectangular cuboid or simply a box) is a 3D solid with six rectangular faces, all angles being 90 degrees.
Key Formulas
- Volume: V = length x width x height
- Surface Area: SA = 2(lw + lh + wh)
- Space Diagonal: d = sqrt(l² + w² + h²)
- Lateral Surface Area: LA = 2h(l + w) (just the four sides, no top or bottom)
Example
A box that is 5 x 3 x 4:
- Volume = 60 cubic units
- Surface Area = 2(15 + 20 + 12) = 94 square units
- Space diagonal = sqrt(25 + 9 + 16) = sqrt(50) = 7.071 units
Practical Uses
- Shipping: Volume tells you capacity, surface area tells you how much wrapping or cardboard you need
- Construction: Concrete volume for foundations, paint for walls (lateral area)
- Storage: Whether an object fits inside a box (check the space diagonal for long items)
- Aquariums: Volume determines water capacity; 1 gallon = 231 cubic inches