Geometry

Surface Area Calculator

Calculate the surface area of any 3D shape — cube, cuboid, cylinder, sphere or cone — with full step-by-step working. The calculator shows the formula for each face and how they are combined.

Shape

Length (l)

Width (w)

Height (h)

Surface area of Cuboid

94 units²

How it works

Formula
$SA = 2(lw + lh + wh)$
Sum of areas of all 6 rectangular faces.
Calculate each pair
lw = 20, lh = 15, wh = 12.
Total
$SA = 2(20 + 15 + 12) = 94$
SA = 94 square units.
Result:94 units²

Surface area formulas

SA_{\text{cuboid}} = 2(lw+lh+wh) \quad SA_{\text{cyl}} = 2\pi r(r+h) \quad SA_{\text{sphere}} = 4\pi r^2

l, w, h

Length, width, height

r

Radius

Worked examples

Find the surface area of a cube with side 4 cm.

1
Formula: SA = 6s²
2
Substitute: SA = 6 × 16
3
Calculate: 96 cm²

Answer: 96 cm²

Find the surface area of a cylinder with radius 3 cm and height 8 cm.

1
Formula: SA = 2πr(r + h)
2
Substitute: SA = 2π × 3(3 + 8) = 6π × 11
3
Calculate: ≈ 207.35 cm²

Answer: ≈ 207.35 cm²

Find the surface area of a sphere with radius 5 cm.

1
Formula: SA = 4πr²
2
Substitute: SA = 4 × π × 25
3
Calculate: ≈ 314.16 cm²

Answer: ≈ 314.16 cm²

Frequently asked questions

What is the surface area of a cylinder?+

Surface area = 2πr² + 2πrh (two circles plus the curved surface).

What is the surface area of a sphere?+

Surface area = 4πr².

What is the surface area of a cuboid?+

Surface area = 2(lw + lh + wh), where l = length, w = width, h = height.

What is the curved surface area of a cone?+

Curved surface area = πrl, where r is the radius and l is the slant height.

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