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

Calculate the total surface area of a cuboid (rectangular box) by entering its three dimensions. The calculator applies the standard formula SA = 2(lw + lh + wh) and breaks down the contribution of each pair of faces.

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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
-
cm²

Top + Bottom (2lw)

cm²

Front + Back (2lh)

cm²

Left + Right (2wh)

cm²

Face-by-Face Breakdown

Length (l)-

Width (w)-

Height (h)-

Top face (l x w)-

Front face (l x h)-

Side face (w x h)-

Total surface area-

Additional Properties

Volume (l x w x h)-

Face diagonal (lw face)-

Face diagonal (lh face)-

Face diagonal (wh face)-

Space diagonal-

Perimeter of base (2l + 2w)-

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.

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