Cone Frustum Surface Area Calculator
From two radii and a height, get the slant height, the curved (lateral) surface area, and the total surface area of a truncated cone.
Three inputs, three answers
Enter the bottom radius, top radius, and height and the calculator returns the slant height (√((R−r)²+h²)), the lateral surface (π(R+r)l), and the total surface (lateral + πR² + πr²) at once.
Keep units consistent
The two radii and the height are unit-agnostic — your surfaces come back in square units of whatever length unit you use, so don't mix centimetres with inches.
What is a cone frustum surface area calculator?
Two radii and a height in, full surface out
A conical frustum is what you get when you slice the tip off a cone with a cut parallel to its base — a bucket shape, a lampshade, a flower pot, a paper coffee cup. It has two circular faces: a larger one at the bottom (radius R) and a smaller one at the top (radius r), separated by a vertical height h. This calculator turns those three measurements into the surface areas you actually need: the slant height (the diagonal side), the lateral surface (the curved wall by itself), and the total surface (the curved wall plus both circular caps). Each one is fixed once you know R, r, and h, so these three inputs are all you need for craft templates, sheet-metal layouts, paint estimates, and geometry homework.
Enter the bottom radius, top radius, and height in any length unit to get the slant height, lateral surface, and total surface instantly.
Three short formulas, all built from the two radii, the height, and the constant π (about 3.14159).
total = π × (R + r) × l + π × R² + π × r²The slant height l is the diagonal side of the frustum; because the radius shrinks by (R − r) over the height h, the Pythagorean theorem gives l = √((R − r)² + h²). The lateral surface — the curved wall, neither cap — is π × (R + r) × l. The total surface adds the two flat circles: the bottom face π × R² and the top face π × r².
Suppose you have a frustum with a bottom radius of 5, a top radius of 3, and a height of 4.
Slant height
√((5 − 3)² + 4²) = √(4 + 16) = √20 ≈ 4.472136 — the diagonal side.
Lateral surface
π × (5 + 3) × 4.472136 ≈ 112.397036 square units — the curved wall only.
Total surface
112.397036 + π × 5² + π × 3² ≈ 219.211186 square units — wall plus both caps.
The three outputs answer three different practical questions. The slant height (about 4.472136 here) is the distance you would measure down the sloping outside of the frustum from the top rim to the bottom rim — it is what you mark out when you cut a flat template to roll into a bucket or lampshade, and it is always longer than the vertical height. The lateral surface (about 112.397036 square units) is the curved wall on its own: the material in a lampshade, the label wrapped around a tapered cup, the metal in the side of a bucket — use this when the ends are open. The total surface (about 219.211186 square units) adds both flat circles, so it is the figure you want when the frustum is closed top and bottom, like the full outside of a sealed container you need to paint or coat. Notice the lateral surface uses the sum of the radii (R + r), which is the same as twice the average radius — the curved wall behaves like a cylinder whose radius is the average of the top and bottom. If the two radii are equal, the frustum becomes a plain cylinder and the formulas collapse to the familiar cylinder surface.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Right circular frustums and consistent units
These formulas describe a right circular frustum — both faces are circles and the axis between their centres is vertical. An oblique frustum (the top circle shifted off to one side), an elliptical or square-tapered shape, or a real object with a rolled lip or wall thickness will differ from the computed value. The height here is the vertical height between the faces, not the slant — don't swap them. The two radii and the height are also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: radii and a height in centimetres give surfaces in square centimetres, never a mix.