Enter your rectangular prism's length, width, and height to calculate its total surface area. You'll also get a breakdown of the lateral surface area, top/bottom face area, front/back face area, and left/right face area — plus the space diagonal and volume.
Total Surface Area
--
Lateral Surface Area
--
Top & Bottom Face Area (each)
--
Front & Back Face Area (each)
--
Left & Right Face Area (each)
--
Volume
--
Space Diagonal
--
A rectangular prism (also called a cuboid) is a three-dimensional geometric shape with six rectangular faces. All angles are right angles, and opposite faces are equal in area. Common examples include boxes, bricks, and rooms.
The total surface area is calculated as S = 2(lw + lh + wh), where l is length, w is width, and h is height. This accounts for all six rectangular faces: two top/bottom faces (lw each), two front/back faces (lh each), and two left/right faces (wh each).
The lateral surface area includes only the four side faces of the prism — it excludes the top and bottom faces. It is calculated as S_lat = 2h(l + w). The total surface area adds the top and bottom faces: S_tot = S_lat + 2lw.
Simply plug your length (l), width (w), and height (h) into the formula S = 2(lw + lh + wh). For example, a box with dimensions 4 × 4 × 10 has a surface area of 2(16 + 40 + 40) = 2(96) = 192 square units.
Using S = 2(lw + lh + wh) = 2(4×4 + 4×10 + 4×10) = 2(16 + 40 + 40) = 2 × 96 = 192 square units.
The space diagonal is the longest straight-line distance from one corner of the prism to the opposite corner, passing through the interior. It is calculated as d = √(l² + w² + h²). This is analogous to the hypotenuse of a 3D right triangle.
The surface area result is in square units — whatever unit you use for length, width, and height. If your dimensions are in centimeters, the surface area is in cm². The calculator does not convert between units, so make sure all three inputs use the same unit.
Yes. A cube is a rectangular prism where all three dimensions are equal (l = w = h). In that case, all six faces are identical squares, and the total surface area simplifies to S = 6l².