Surface Area Calculator
Calculate the total surface area of common 3D shapes: cube, rectangular box, sphere, cylinder and cone.
- Top & Bottom48 · 44%
- Front & Back36 · 33%
- Left & Right24 · 22%
A box's surface splits into three pairs of matching faces — the largest pair here contributes 44% of the total area.
ƒShow your work
SA = 2(lw + lh + wh)
About the Surface Area Calculator
Surface area is the total area covering the outside of a 3D shape — every face, added together. It's the number that actually matters when you're covering, wrapping, painting, or plating something, as opposed to volume, which tells you how much a shape holds on the inside.
It's a standard geometry-class topic across cubes, boxes, spheres, cylinders and cones, but it's also genuinely practical: figuring out how much wrapping paper a box needs, how much paint a cylindrical tank's exterior requires, how much material goes into a can or a cone-shaped container, or how much fabric covers a spherical shape.
Each shape has its own formula because each is built from a different combination of flat and curved faces, but they all reduce to the same idea — add up the area of every face that makes up the shape's outer surface.
How it’s calculated
A cube's surface area is 6 × side², since all six faces are identical squares. A rectangular box generalizes that into three pairs of matching rectangular faces: SA = 2(lw + lh + wh), where each term covers one pair (top/bottom, front/back, left/right).
A sphere's surface area, 4πr², comes from calculus but is simple to apply — it depends only on the radius. A cylinder splits into two flat circular ends (2πr²) plus one curved rectangular side wrapped around (2πrh), combining to SA = 2πr(r + h). A cone splits similarly into a flat circular base (πr²) plus a curved lateral surface (πr × slant height, where the slant height is √(r² + h²) by the Pythagorean theorem).
Frequently asked questions
What's the difference between surface area and volume?
Surface area measures the total area of a shape's outer faces — think of it as how much material would wrap the outside. Volume measures how much space the shape encloses on the inside. They're measured in different units too: surface area in square units, volume in cubic units.
Why does a cone need the slant height instead of the regular height?
The cone's curved side is slanted, not vertical, so its area depends on the distance along that slanted surface (the slant height) rather than the straight vertical height — the two are only equal for a perfectly flat cone, which isn't really a cone at all.
How do you find the surface area of a cylinder?
Add the area of the two circular ends (2πr²) to the area of the curved side unrolled into a rectangle (2πrh, where h is the height): SA = 2πr(r + h).
Is surface area always in square units?
Yes — since it's an area measurement, the result is always in square units (square inches, square meters, etc.), regardless of which 3D shape you're measuring.
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