Surface Area of a Cuboid
Total surface area of a rectangular box.
Formula
Live Calculator
MembersVariables
Example
A 2 × 3 × 4 box: A = 2(6+8+12) = 52 square units.
How it works
A cuboid has 6 rectangular faces: two length-by-width faces, two length-by-height faces, and two width-by-height faces. The formula adds the area of each pair of opposite faces, which is why each product appears twice and is multiplied by 2. This gives the total amount of material needed to cover the outside of the box.
When to use it
Use this when you need the outside area of a rectangular box, such as wrapping a package, painting a box-shaped object, or finding how much cardboard is needed to make a container. It is also useful in geometry problems involving rectangular prisms.
Worked example, step by step
Find the surface area of a cuboid with l = 5 cm, w = 2 cm, and h = 3 cm. A = 2(lw + lh + wh) A = 2((5)(2) + (5)(3) + (2)(3)) A = 2(10 + 15 + 6) A = 2(31) A = 62 cm²
Common mistakes to avoid
- Forgetting that there are two of each rectangular face
- Using the volume formula instead of surface area
- Not squaring the units, so writing cm instead of cm²
Did You Know?
A cardboard box unfolds into six rectangles — add their areas and you have the surface area.
Share this formula
More in Geometry & Trigonometry
View allPythagorean Theorem
BasicRelates the sides of a right triangle.
Area of a Circle
BasicThe area enclosed by a circle.
Circumference of a Circle
BasicThe perimeter (boundary length) of a circle.
Equation of a Circle
IntermediateThe standard form of the equation of a circle with centre (h, k) and radius r.
Area of a Rectangle
BasicArea of a rectangle.
Area of a Triangle
BasicArea of a triangle from base and height.