Surface Area Formulas

Surface area formulas total the area of every outer face of a solid, in square units. The essentials are cube SA = 6s², cylinder SA = 2πr(r + h), cone SA = πr(r + ℓ), and sphere SA = 4πr². The table below covers each common solid, with a live explorer behind every shape name.

All 3D surface-area formulas

Solid	Surface area	Lateral / curved
Cube	$SA = 6s^2$
Rectangular Prism	$SA = 2(lw + lh + wh)$
Triangular Prism	$SA = 2A_{base} + (a+b+c)L$
Cylinder	$LSA = 2\pi r h$ $SA = 2\pi r(r + h)$	$LSA = 2\pi r h$
Cone	$LSA = \pi r \ell$ $SA = \pi r(r + \ell)$	$LSA = \pi r \ell$
Sphere	$SA = 4\pi r^2$
Hemisphere	$2\pi r^2$ $SA = 3\pi r^2$	$2\pi r^2$
Pyramid	$LSA = 2 b \ell$ $SA = b^2 + 2 b \ell$	$LSA = 2 b \ell$

Worked examples

Cube side 2: SA = 6s² = 6·4 = 24 square units.
Cylinder r = 3, h = 6: SA = 2πr(r + h) = 2π·3·9 = 54π ≈ 169.65.
Cone r = 3, ℓ = 5: SA = πr(r + ℓ) = π·3·8 = 24π ≈ 75.40.
Sphere r = 5: SA = 4πr² = 100π ≈ 314.16.

Variable glossary

a, b, cside lengths
l, w, hlength, width, height
rradius
ddiameter (d = 2r)
sside length or slant height
ℓslant height
bbase
Pperimeter
Ccircumference
Aarea
SAsurface area
Vvolume
θcentral angle (degrees)

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Frequently asked questions

What is surface area?

Surface area is the total area of all the outer faces of a solid, measured in square units. For a cube it is SA = 6s² (six equal square faces); for a sphere it is SA = 4πr².

What is the difference between lateral and total surface area?

Lateral surface area covers only the sides of a solid, excluding its base(s). Total surface area adds the base(s). For a cylinder, lateral = 2πrh and total = 2πr(r + h).

What is the surface area of a cone?

A cone’s total surface area is SA = πr(r + ℓ), where ℓ = √(r² + h²) is the slant height — the base circle πr² plus the curved lateral surface πrℓ.