Math
Rectangular Prism Calculator
Calculate volume, surface area, base area, lateral area, and space and face diagonals of a rectangular prism (box) from length, width, and height.
Rectangular prism dimensions
Volume
60
- Surface area
- 94
- Lateral surface area
- 70
- Base area
- 12
- Base perimeter
- 14
- Space diagonal
- 7.0711
- Face diagonal (l, w)
- 5
- Face diagonal (l, h)
- 5.831
- Face diagonal (w, h)
- 6.4031
Frequently Asked Questions about the Rectangular Prism Calculator
How do you calculate the volume of a rectangular prism?
Volume equals length x width x height. Multiply the three side dimensions together using the same unit. For a 3 x 4 x 5 inch box, the volume is 60 cubic inches. A rectangular prism is also called a cuboid or a box, and the formula works for any orientation as long as the three edges meet at right angles.
What is the surface area formula for a box?
Surface area equals 2 x (lw + lh + wh), where l, w, and h are length, width, and height. The formula adds the areas of all six rectangular faces: two of size lw, two of size lh, and two of size wh. For a 3 x 4 x 5 box that is 2 x (12 + 15 + 20) = 94 square units.
What is the difference between surface area and lateral surface area?
Surface area includes all six faces. Lateral surface area covers only the four side walls and leaves out the top and bottom: 2 x h x (l + w). Pick lateral when you are wrapping a label around a box or calculating side panels for a tank, and pick full surface area when the lid and base are also part of the job.
How do you find the space diagonal of a rectangular prism?
The space diagonal goes from one corner of the box straight through the interior to the opposite corner. Its length is sqrt(l^2 + w^2 + h^2), an extension of the Pythagorean theorem to three dimensions. For a 3 x 4 x 5 box that is sqrt(50), about 7.07 units.
When is a rectangular prism a cube?
A cube is the special case where all three edges are equal. The formulas simplify to V = s^3, surface area = 6 s^2, and space diagonal = s x sqrt(3). For a 5 x 5 x 5 cube the volume is 125, the surface area is 150, and the space diagonal is about 8.66.