Surface Area Calculator

Wrap-a-solid math made instant: five standard solids with exact formulas — cone slant height included automatically.

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How to use

  1. Choose the solid from the dropdown.
  2. Fill in the edge, radius or height fields that appear.
  3. The total surface area updates instantly as you type.

Frequently asked questions

Which solids are supported?

Five: cube (6a²), cuboid (2(lw + lh + wh)), sphere (4πr²), cylinder (2πr² + 2πrh) and cone (πr² + πr·l, where the slant height l = √(r² + h²) is computed for you).

What is the slant height of a cone?

It is the distance from the rim to the apex along the cone’s surface — the hypotenuse of the right triangle formed by the radius and the axis height. This tool derives it automatically from r and h.

Why does a cylinder include both ends?

Total surface area counts the closed solid: the tube (2πrh) plus both circular caps (2πr²). For an open tube like a pipe segment, subtract one or both caps yourself — the calculator reports the standard closed-solid value.

How is surface area different from volume?

Surface area measures the material needed to wrap a solid (units squared); volume measures what it can hold (units cubed). Doubling every edge quadruples surface area but multiplies volume by eight.

Can I use these formulas for real material estimates?

They give exact geometric values — good for paint, wrapping or sheet metal first-passes. Real-world factors like overlaps, seams and waste mean you should add a margin before ordering material.

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