Surface Area of Cuboids

In a Nutshell

Surface area is the total area of all the faces of a 3D shape. A cuboid has six rectangular faces that come in three matching pairs.

Imagine unfolding a cuboid into its net. You get six rectangles. The three pairs of opposite faces are:

  • Top and bottom: each l×wl \times w
  • Front and back: each l×hl \times h
  • Left and right: each w×hw \times h
SA=2lw+2lh+2wh=2(lw+lh+wh)\text{SA} = 2lw + 2lh + 2wh = 2(lw + lh + wh)

Surface area is measured in square units (e.g. cm2\text{cm}^2), even though the shape is 3D, because each face is a flat area.

Explore: cuboid net

Cuboid unfolding into a net A 3D cuboid unfolds into a cross-shaped net. Opposite faces share colours: blue for top and bottom, green for front and back, orange for left and right. The surface area formula updates live.

Enter the length, width and height, then press Calculate SA to see each face area and the total surface area.

Watch it work

Question: Find the surface area of a cuboid with l=5 cml = 5 \, \text{cm}, w=3 cmw = 3 \, \text{cm} and h=2 cmh = 2 \, \text{cm}.

Have a go

Q1. Find the surface area of a cuboid with l=4l = 4, w=3w = 3, h=2h = 2 (cm).

Q2. A cube has side 5 cm5 \, \text{cm}. Find its surface area.

Q3. A cereal box is 30 cm30 \, \text{cm} tall, 20 cm20 \, \text{cm} wide and 8 cm8 \, \text{cm} deep. How much cardboard is needed to make it?

Q4. A cuboid has surface area 94 cm294 \, \text{cm}^2, length 5 cm5 \, \text{cm} and width 3 cm3 \, \text{cm}. Find the height.