Surface Area Formulas for 3D Shapes

Direct answer

What is a surface area formula?

Surface area formulas calculate the total outside area of a 3D solid. Common examples include cube surface area $S A = 6 s^{2}$ , cylinder total surface area $T S A = 2 π r (r + h)$ , and sphere surface area $S A = 4 π r^{2}$ . Use square units, and for prisms add the areas of all outside faces.

Quick table

Surface area formulas table

Shape	Formula	Use
Cube	$S A = 6 s^{2}$	s = side length
Rectangular prism	$S A = 2 (l w + l h + w h)$	l = length, w = width, h = height
Cylinder total surface area	$T S A = 2 π r (r + h)$	r = radius, h = height
Cylinder lateral surface area	$L S A = 2 π r h$	Curved side only
Cone total surface area	$T S A = π r (r + l)$	l = slant height
Cone lateral surface area	$L S A = π r l$	Curved side only
Sphere	$S A = 4 π r^{2}$	r = radius

Formula cards

Quick formula cards

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Circle Formulas

Area $A = π r^{2}$

Circumference $C = 2 π r = π d$

Diameter $d = 2 r$

Radius $r = \frac{d}{2}$

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Triangle Formulas

Area $A = \frac{1}{2} bh$

Perimeter $P = a + b + c$

Right triangle $a^{2} + b^{2} = c^{2}$

Heron's formula $A = s (s - a) (s - b) (s - c)$

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Cylinder Formulas

Volume $V = π r^{2} h$

Lateral surface area $L S A = 2 π r h$

Total surface area $T S A = 2 π r (r + h)$

Base area $B = π r^{2}$

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Cone Formulas

Volume $V = \frac{1}{3} π r^{2} h$

Lateral surface area $L S A = π r l$

Total surface area $T S A = π r (r + l)$

Slant height $l = r^{2} + h^{2}$

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Sphere Formulas

Volume $V = \frac{4}{3} π r^{3}$

Surface area $S A = 4 π r^{2}$

Diameter $d = 2 r$

Radius $r = \frac{d}{2}$

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Examples

Step-by-step examples

Cube surface area

Given s = 4 cm.
Use $S A = 6 s^{2}$ .
$S A = 6 \times 16 = 96 c m^{2}$ .

Cylinder total surface area

Given r = 3 m and h = 5 m.
Use $T S A = 2 π r (r + h)$ .
$T S A = 2 π \times 3 (3 + 5) = 48 π \approx 150.80 m^{2}$ .

Sphere surface area

Given r = 7 in.
Use $S A = 4 π r^{2}$ .
$S A = 196 π \approx 615.75 i n^{2}$ .

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FAQ

Surface Area Formulas FAQ

What does total surface area mean?

Total surface area includes every outside face or curved surface of a 3D object.

What does lateral surface area mean?

Lateral surface area usually excludes the base or bases and measures only the side surface.

Does surface area use square or cubic units?

Surface area uses square units because it measures area, not volume.