Cuboid Surface Area Calculator

A cuboid is a solid with six rectangular faces that meet at right angles. A rectangular prism is the same shape under another name, so a formula for one works for the other. Cartons, rooms, fish tanks, shipping containers and bricks are all cuboids. Each input has its own unit menu, so a length in feet and a height in inches can be entered as measured.

Formula

A = 2 × (l × w + l × h + w × h)

A

the total surface area

l

the length

w

the width

h

the height

The lateral area, the four sides alone, is 2 × h × (l + w).

Surface area of a closed box

The faces come in three matching pairs: top and bottom, front and back, left and right. Find one of each, add them and double the total. A box 5 ft long, 3 ft wide and 2 ft high has faces of 15, 10 and 6 ft², so its surface is 2 × 31 = 62 ft². A shoebox of 33 × 19 × 12 cm has 2 × (627 + 396 + 228) = 2,502 cm² of card on the outside.

Surface area of an open-top tank

With no lid, the top face drops out, leaving the base and four walls. The same 5 × 3 × 2 box has 62 − 15 = 47 ft² of surface once its top is gone. That is the figure to use for lining a planter or waterproofing a pond tank.

A rectangular tank 2 m long, 1 m wide and 1.5 m deep has a base of 2 m² and walls of 2 × 1.5 × 3 = 9 m², so 11 m² in all. It holds 3 m³, which is 3,000 liters. To coat the inside and the outside, double the area. The calculator treats the walls as thin, so for thick concrete or masonry, measure the inner and outer faces separately.

• A = l × w + 2 × h × (l + w)

Lateral area

Lateral area means the four sides only, without the top or the bottom. Unfold them and they form one long rectangle, as tall as the box and as long as the distance around its base, which is where 2 × h × (l + w) comes from. For a room this is the wall area: 14 ft by 11 ft with an 8 ft ceiling gives 2 × 8 × 25 = 400 ft² before you subtract doors and windows.

• Lateral area = 2 × h × (l + w)

Space diagonal and volume

The result also shows the space diagonal, the longest straight line inside the box, from one corner to the opposite corner. It tells you whether a long object will fit. In the 5 × 3 × 2 box it is √(25 + 9 + 4) ≈ 6.16 ft. The volume is simply length times width times height, 30 ft³ here. For other solids, use the volume calculator.

• d = √(l² + w² + h²)
• V = l × w × h

Same volume, different surface

Boxes with the same capacity can need very different amounts of material. A 1 × 1 × 8 box and a 2 × 2 × 2 box both hold 8 cubic units, but the first has a surface of 34 and the second only 24. The closer a box is to a cube, the less material it uses. When all three sides are equal, the cube surface area calculator gives the same answer with one input.

Frequently asked questions