Cone Calculator

The slant height equals the square root of the radius squared plus the height squared, l = sqrt(r^2 + h^2). This follows from the Pythagorean theorem applied to the right triangle formed by the radius, the vertical height, and the slant side.

Yes. The total surface area combines the curved lateral surface pi*r*l and the flat circular base pi*r^2. Subtract the base area if you only need the lateral surface, for example when sizing a paper cone or a wrap.

The volume is V = (1/3) x pi x r^2 x h, using the base radius r and the vertical height h. A cone always holds exactly one third the volume of a cylinder with the same base and height. Keep the radius and height in the same unit so the volume comes out in cubic units.

A cone has exactly one third the volume of a cylinder with the same base radius and height: V = (1/3)πr²h. In other words, three cones fill one matching cylinder.

A frustum is a cone with the top cut off. Its volume is V = (1/3)πh(R² + Rr + r²), where R and r are the two circular radii and h is the height between them; it reduces to the cone formula when r = 0.