Rectangular Prism Calculator

A rectangular prism (also called a cuboid) is a three-dimensional solid with six rectangular faces. Every pair of opposite faces is identical, and all interior angles are right angles. Common real-world examples include boxes, bricks, and rooms.

Volume is calculated as V = l × w × h, where l is the length, w is the width, and h is the height. Simply multiply the three dimensions together. The result is expressed in cubic units (e.g., cm³ or ft³).

The total surface area is S = 2(lw + lh + wh). This formula accounts for all six faces: two top/bottom faces (l × w each), two front/back faces (l × h each), and two side faces (w × h each). The result is expressed in square units.

The space diagonal runs from one corner of the prism to the opposite corner through the interior. It is calculated using d = √(l² + w² + h²), which extends the Pythagorean theorem into three dimensions.

The lateral surface area covers only the four side faces, excluding the top and bottom. The formula is S_lat = 2h(l + w). This is useful when you need to know, for example, how much material wraps around the sides of a box without the lids.

A cube is a special case of a rectangular prism where all three dimensions are equal (l = w = h). Every cube is a rectangular prism, but not every rectangular prism is a cube. For a cube with side s, volume = s³ and surface area = 6s².

A rectangular prism has 6 faces (all rectangles), 12 edges, and 8 vertices (corners). The 12 edges come in three groups of 4 parallel edges — four of length l, four of width w, and four of height h.

No — you need all three dimensions (length, width, and height) to calculate volume, surface area, or diagonal. If you only know one dimension along with additional constraints like the total volume or surface area, you can solve for the others algebraically.