Surface Area of a Rectangular Prism Calculator
Calculate the total surface area, lateral surface area, base area, volume, and space diagonal of a rectangular prism (box). Just enter the length, width, and height to get instant results.
A rectangular prism (also called a cuboid or box) has six rectangular faces. The total surface area is the sum of the areas of all six faces.
Total Surface Area Formula
SA = 2(lw + lh + wh)
This accounts for three pairs of identical faces: top/bottom (l x w), front/back (l x h), and left/right (w x h).
Lateral Surface Area
The lateral surface area includes only the four side faces, excluding the top and bottom: LSA = 2h(l + w). This is useful when calculating how much material you need to wrap the sides of a box.
Space Diagonal
The space diagonal runs from one corner of the box to the opposite corner, passing through the interior. It equals sqrt(l² + w² + h²). This extends the Pythagorean theorem to three dimensions.
Practical Applications
Knowing the surface area of a box helps you figure out how much wrapping paper, paint, or material you need. Shipping companies use surface area and volume together to determine packaging costs.