What is the formula for the surface area of a cuboid?

The total surface area of a cuboid is SA = 2(lw + lh + wh), where l is length, w is width, and h is height. A cuboid has six rectangular faces: two faces of lw (top and bottom), two of lh (front and back), and two of wh (left and right). Summing all six faces gives the total surface area.

What is the difference between a cuboid and a cube?

A cube is a special case of a cuboid where all three dimensions (length, width, and height) are equal. The surface area of a cube simplifies to 6s², where s is the side length. For a general cuboid, the three dimensions can be different, so the full formula SA = 2(lw + lh + wh) is needed.

What units does this cuboid surface area calculator use?

The calculator works with any consistent unit. If you enter dimensions in centimetres, the surface area is in square centimetres (cm²). If you use metres, the result is in square metres (m²). Simply choose a unit label from the dropdown to display the correct unit alongside your result.

Cuboid Surface Area Calculator

This calculator works out the total surface area of a cuboid (a rectangular box, also known as a rectangular prism) using the standard formula SA = 2(lw + lh + wh). You enter the length, width and height, then choose a unit of measurement from millimetres, centimetres, metres, inches or feet. The calculator instantly returns the total surface area, plus a breakdown of the three pairs of faces: top and bottom (2lw), front and back (2lh), and left and right (2wh). A detailed table below also shows each individual face area, the volume of the box, the diagonal length across each of the three faces, the space diagonal running corner to corner through the middle, and the perimeter of the base. This makes it useful for anything involving a box-shaped object, from working out how much cardboard or wrapping paper you need, to estimating the glass for an aquarium, insulation material, or paint for a tank or storage container. Make sure all three dimensions use the same unit, since mixing centimetres and metres will throw the result out. A cube is simply a special case of a cuboid where all three sides are equal, so if your shape is a perfect cube, enter the same value for length, width and height and the calculator handles it just the same.

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Standard formula SA = 2(lw + lh + wh). Works in any consistent unit (mm, cm, m, inches, feet).

1. Dimensions

Length (l)

Width (w)

Height (h)

2. Unit

Unit of measurement

Formula: SA = 2(lw + lh + wh)
Where l = length, w = width, h = height

Surface Area Results

Total Surface Area
62
cm²

Top + Bottom (2lw)

cm²

Front + Back (2lh)

cm²

Left + Right (2wh)

cm²

Face-by-Face Breakdown

Length (l)5 cm

Width (w)3 cm

Height (h)2 cm

Top face (l x w)15 cm2

Front face (l x h)10 cm2

Side face (w x h)6 cm2

Total surface area62 cm2

Additional Properties

Volume (l x w x h)30 cm3

Face diagonal (lw face)5.831 cm

Face diagonal (lh face)5.3852 cm

Face diagonal (wh face)3.6056 cm

Space diagonal6.1644 cm

Perimeter of base (2l + 2w)16 cm

How to Calculate the Surface Area of a Cuboid

A cuboid (also called a rectangular prism or rectangular box) has six rectangular faces arranged in three opposite pairs. The total surface area is found by adding the area of all six faces.

The formula is: SA = 2(lw + lh + wh)

lw is the area of the top (or bottom) face. There are two of these, giving 2lw.
lh is the area of the front (or back) face. There are two of these, giving 2lh.
wh is the area of the left (or right) face. There are two of these, giving 2wh.

Worked Example

For a cuboid with length 5 cm, width 3 cm, and height 2 cm:

Top + Bottom: 2 x (5 x 3) = 2 x 15 = 30 cm²
Front + Back: 2 x (5 x 2) = 2 x 10 = 20 cm²
Left + Right: 2 x (3 x 2) = 2 x 6 = 12 cm²
Total SA = 30 + 20 + 12 = 62 cm²

This matches the calculator's default output when l = 5, w = 3, h = 2.

Units

The surface area unit is always the square of the length unit. If you measure in centimetres, the result is in cm². If you measure in metres, the result is in m². Use consistent units for all three dimensions: do not mix centimetres and metres in the same calculation.

Cuboid vs Cube

A cube is a special cuboid where l = w = h = s. Its surface area simplifies to 6s². For any other cuboid with unequal dimensions, you must use the full formula SA = 2(lw + lh + wh).

Common Applications

Application	Why Surface Area Matters
Packaging and boxes	Determines how much cardboard or material is needed
Painting a room	Used alongside wall area calculations to estimate paint volume
Insulation	Calculates the total area needing insulation material
Aquariums and tanks	Helps estimate glass area and heat transfer
Gift wrapping	Estimates how much wrapping paper is required

Related Calculators

Maths and Stats Calculators: all geometry and measurement tools.
Cube Surface Area and Volume Calculator: for the special case where all sides are equal.
Rectangular Box (Cuboid) Calculator: volume, surface area, and diagonals in one tool.
Pyramid Volume and Surface Area Calculator: surface area for pyramid shapes.
Volume Calculator (multi-solid): volume for many 3D shapes.

Method: Standard Euclidean geometry formula SA = 2(lw + lh + wh). Face diagonal = sqrt(a² + b²). Space diagonal = sqrt(l² + w² + h²). Results are exact for the dimensions entered.