What is the difference between total and lateral surface area?

Total surface area covers every face including the top and bottom, while lateral surface area is just the curved or slanted side. The calculator reports both for cylinders and cones; for a cube and sphere only the total is shown.

Why does the cone need a slant height instead of vertical height?

The lateral surface of a cone wraps along its slanted edge, so its area depends on the slant height l, not the vertical height. If you only know the vertical height h and radius r, the slant height is √(r² + h²).

What units does the result use?

Surface area is always in square units of whatever you entered — if your dimensions are in centimetres the area is in square centimetres. The calculator does not assume a unit; it simply works in whatever you provide.

How is surface area different from volume?

Surface area measures the two-dimensional skin of a shape (in square units), while volume measures the three-dimensional space inside it (in cubic units). For the same shapes you can compute the interior space with the volume calculator.

Surface Area Calculator

Shape

Side Length

Surface Area150.0000

Surface area is the total area of the outer faces of a three-dimensional shape — the amount of material needed to cover it. This calculator computes the surface area of a cube, sphere, cylinder, or cone from the relevant dimensions, and for the cylinder and cone it also separates out the lateral (side) area from the total.

Formula

Cube 6s² · Sphere 4πr² · Cylinder 2πr(r + h) · Cone πr(r + l)

s: Side length of the cube
r: Radius of the sphere, cylinder, or cone
h: Height of the cylinder
l: Slant height of the cone (not its vertical height)

How it works

Choose a shape: cube (enter side length), sphere (radius), cylinder (radius and height), or cone (radius and slant height).
Each shape uses its standard surface-area formula — for example 6s² for a cube and 4πr² for a sphere.
For a cylinder the total is 2πr(r + h) with a lateral area of 2πrh; for a cone the total is πr(r + l) with a lateral area of πrl. Any non-positive dimension is invalid and returns no result.

Worked examples

Find the surface area of a cylinder with radius 3 and height 5.

Total = 2πr(r + h) = 2π × 3 × (3 + 5) = 2π × 3 × 8 = 48π.
48π ≈ 150.7964.
Lateral area = 2πrh = 2π × 3 × 5 = 30π ≈ 94.2478.

Total surface area ≈ 150.80, lateral area ≈ 94.25

Find the surface area of a sphere with radius 4.

Surface area = 4πr² = 4π × 4² = 4π × 16 = 64π.
64π ≈ 201.0619.
A sphere has no separate lateral area.

Surface area ≈ 201.06

Frequently asked questions

What is the difference between total and lateral surface area?: Total surface area covers every face including the top and bottom, while lateral surface area is just the curved or slanted side. The calculator reports both for cylinders and cones; for a cube and sphere only the total is shown.
Why does the cone need a slant height instead of vertical height?: The lateral surface of a cone wraps along its slanted edge, so its area depends on the slant height l, not the vertical height. If you only know the vertical height h and radius r, the slant height is √(r² + h²).
What units does the result use?: Surface area is always in square units of whatever you entered — if your dimensions are in centimetres the area is in square centimetres. The calculator does not assume a unit; it simply works in whatever you provide.
How is surface area different from volume?: Surface area measures the two-dimensional skin of a shape (in square units), while volume measures the three-dimensional space inside it (in cubic units). For the same shapes you can compute the interior space with the volume calculator.

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Volume Calculator Circle Calculator Area Calculator Hemisphere Calculator