Surface Area Calculator
Wrap-a-solid math made instant: five standard solids with exact formulas — cone slant height included automatically.
How to use
- Choose the solid from the dropdown.
- Fill in the edge, radius or height fields that appear.
- 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.