Surface Area in Math: Definition, Formulas & Examples

Definitionnoun phrase

What is surface area in math?

Surface area is the total area of all outside faces of a three-dimensional figure, measured in square units. To find it, unfold the solid into a flat net, find the area of each face and add them. A box with length l, width w and height h has surface area 2lw + 2lh + 2wh.

In Spanish: área de superficie (área total)
Also called: outside area, total surface area, SA
Grade level: 6-8

Grade 6Grade 7Grade 8CCSS 6.G.A.4CCSS 7.G.B.6GEDSATACT

Surface Area in a picture

Unfold the box into its net and add the six faces: 30 + 20 + 12 = 62 square units. Each face appears twice, once on each side of the box.

Formal definition and notation

The surface area of a solid is the sum of the areas of all the surfaces that bound it. For a polyhedron it is the sum of the areas of its faces, which can be found from a net. For a right prism, SA = 2B + Ph, where B is the base area and P the base perimeter; for a cylinder, SA = 2π r² + 2π r h; for a sphere, SA = 4π r².

Symbol	Read it as	Meaning
SA or S	S A	surface area
cm²	square centimeters	a square unit, the unit of any area
LA	L A	lateral area: the sides only, without the top and bottom

Key facts

Surface area uses square units, while volume uses cubic units.
A net is a flat pattern that folds into the solid; its area equals the surface area.
Opposite faces of a box are equal, so find three face areas and double the total.
Two boxes with the same volume can have different surface areas: a 1 by 1 by 8 box has 34 square units, a 2 by 2 by 2 cube only 24.
Real uses: paint, wrapping paper, the label on a can, the material for a tent.

Surface area formulas

box: SA = 2lw + 2lh + 2wh

SA = 6s²: cube with edge s: six equal square faces
SA = 2B + Ph: any right prism: two bases plus the rectangle wrapped around (base perimeter P times height h)
SA = 2π r² + 2π r h: cylinder: two circles plus the curved side
SA = 4π r²: sphere with radius r

A box has three pairs of matching faces, which is why every term in its formula is doubled. If a box has no lid, leave one face out.

Surface Area examples, step by step

Example 1: Surface area of a cube

Warm-up

A cube has edges of 4 inches. What is its surface area?

A cube has 6 faces, all squares with area 4 × 4 = 16 square inches.
Multiply by 6: 6 × 16 = 96.
Units: area, so square inches.

Answer: The surface area is 96 square inches.

Example 2: Surface area of a box

Core

Find the surface area of a box 8 cm long, 5 cm wide and 3 cm high.

Top and bottom: 2 × (8 × 5) = 80.
Front and back: 2 × (8 × 3) = 48.
Two sides: 2 × (5 × 3) = 30.
Add: 80 + 48 + 30 = 158.

Answer: The surface area is 158 square centimeters.

Example 3: Surface area of a cylinder

Test-style

A closed can has radius 2 cm and height 6 cm. How much metal covers its whole surface, exactly and to the nearest tenth?

Two circles (top and bottom): 2 × π (2)² = 8π.
The side unrolls into a rectangle: width = circumference 2π(2) = 4π, height 6, so area 24π.
Add: 8π + 24π = 32π.
Approximate: 32 × 3.14159 ≈ 100.5.

Answer: The surface area is 32π ≈ 100.5 square centimeters.

Common mistakes

✗ MistakeThe surface area of the box is 158 cubic centimeters.

✓ InsteadIt is 158 square centimeters.

Surface area uses square units, while volume uses cubic units. Surface area is a total of flat areas.

✗ MistakeFor a 5 by 3 by 2 box: 15 + 10 + 6 = 31.

✓ InsteadDouble it: 2(15 + 10 + 6) = 62 square units.

A box has six faces, in three matching pairs. Adding three face areas covers only half the box.

✗ MistakeSurface area of a 5 by 3 by 2 box = 5 × 3 × 2 = 30.

✓ Instead5 × 3 × 2 = 30 is the volume. The surface area is 62.

Multiplying the three dimensions counts cubes inside. Surface area adds the areas of the outside faces.

✗ MistakeAn open-top box 10 by 4 by 3 has surface area 164.

✓ InsteadLeave out the missing top: 164 − 40 = 124 square units.

Surface area counts only the faces that exist. Read whether the box is closed or open.

Not to be confused with

Surface Areavs.Volume

Volume is the space inside, in cubic units; surface area covers the outside, in square units. A 2 by 2 by 2 cube has volume 8 and surface area 24.

Surface Areavs.Area

Area is for one flat shape. Surface area is the total area of every face of a 3D solid.

Surface Areavs.Lateral area

Lateral area counts only the side faces, not the top and bottom. A 5 by 3 by 2 box has lateral area 32 and surface area 62.

Quick check: 3 questions

Question 1 of 3

What is the surface area of a cube with edges of 3 meters?

Show answer and explanation

Answer: C. Six faces of 3 × 3 = 9: 6 × 9 = 54. Choice A is the volume (3³), B is one face, and D counts only four faces.

Question 2 of 3

Which unit could a surface area be measured in?

Show answer and explanation

Answer: A. Surface area is an area, so it uses square units. Cubic centimeters and liters measure volume, and centimeters measure length.

Question 3 of 3

A box with no lid is 10 cm long, 4 cm wide and 3 cm high. What is its outside surface area?

Show answer and explanation

Answer: B. Bottom 40, front and back 2 × 30 = 60, sides 2 × 12 = 24: 40 + 60 + 24 = 124. Choice A includes the missing lid, C is the volume, and D adds just one of each kind of face (40 + 30 + 12).

Surface Area: frequently asked questions

How do you find the surface area of a rectangular prism?

Find the area of the three different faces, lw, lh and wh, add them, and double the sum, because each face has a matching face on the opposite side: SA = 2(lw + lh + wh). For a 6 by 4 by 2 box: 2(24 + 12 + 8) = 88 square units.

What is a net in surface area?

A net is a flat pattern of the faces of a solid that folds up into the solid, like a cereal box cut open and laid flat. Its area is the same as the surface area. Drawing a net helps you see every face once, so you do not miss one or count one twice.

Can two boxes with the same volume have different surface areas?

Yes. A 1 by 1 by 12 box and a 2 by 2 by 3 box both have volume 12 cubic units. Their surface areas are 50 and 32 square units. Compact shapes, close to a cube, use the least surface for a given volume, which is why boxes that save material tend to be cube-like.

Practice and tools

Math practicePractice on Effortless Math Surface Area CalculatorSurface area of prisms, cylinders, cones and spheres Volume CalculatorCompare outside area with inside space Area and Perimeter CalculatorArea of each flat face

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 6.G.A.4, CCSS 7.G.B.6

Cite this entry

Effortless Math Team. “Surface Area.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/surface-area/

Flashcard

TermSurface Areaadd every face

DefinitionTotal area of the outside of a solid, in square units. A cube with edge 2 has surface area 6 × 4 = 24.

Study the full deck

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Surface Area

What is surface area in math?

Surface Area in a picture

Formal definition and notation

Key facts

Surface area formulas

Surface Area examples, step by step

Example 1: Surface area of a cube

Example 2: Surface area of a box

Example 3: Surface area of a cylinder

Common mistakes

Not to be confused with

Quick check: 3 questions

Surface Area: frequently asked questions

How do you find the surface area of a rectangular prism?

What is a net in surface area?

Can two boxes with the same volume have different surface areas?

Related terms

Practice and tools

Sources

Flashcard

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