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Surface Area Calculator

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Choose a shape and enter its dimensions to find its total surface area.

Surface Area Calculator

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Surface area
96

The formulas

Cube: 6 × side² Sphere: 4πr² Cylinder: 2πr² + 2πrh Cone: πr² + πr × slant height Rectangular box: 2(lw + lh + wh)
Example

A cube with 4-unit sides: surface area = 6 × 4² = 96 square units.

Step-by-step guide

  1. Select your shape.
  2. Enter the required dimensions - the fields adjust automatically for your chosen shape.
  3. Read the total surface area.

Why cone surface area only uses slant height, not vertical height

A cone's lateral (curved) surface, if unrolled flat, forms a sector of a circle whose radius is the cone's slant height - not its vertical height. This is why the formula calls specifically for slant height: using vertical height instead would understate the actual surface, since the slant height is always longer (it's the hypotenuse of the right triangle formed by the radius and vertical height). If you only know the vertical height, the slant height can be found first using the Pythagorean theorem before calculating surface area.

Common mistakes

Using diameter instead of radius for spheres and cylinders - these formulas specifically require radius; using diameter directly would overstate the surface area significantly.
Confusing surface area with volume - surface area measures the outer covering (like wrapping paper needed), while volume measures the space inside (like water it can hold). They use different formulas and units.

Frequently asked questions

What's the difference between surface area and volume?

Surface area measures the total area of a shape's outer surface (in square units) - useful for things like paint or wrapping needed. Volume measures the space enclosed inside (in cubic units) - useful for capacity or material fill.

Does this include the base for a cone?

Yes - the cone formula shown includes both the circular base (πr²) and the lateral curved surface (πr × slant height) for the total surface area.

How do I find slant height if I only know the vertical height?

Use the Pythagorean theorem: slant height = √(radius² + vertical height²), since the radius, vertical height, and slant height form a right triangle.

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