A right circular cone is fully defined by just two numbers: its base radius and its height. From those two values alone, you can derive the slant height, the lateral surface area, the total surface area, and the volume — every measurement a cone has. This calculator does that math instantly and shows how each value depends on the others.
How the Cone Calculator works
The calculator starts from the volume formula V = ⅓πr²h, which says a cone holds exactly one-third the volume of a cylinder sharing the same base and height. It then finds the slant height with the Pythagorean theorem, l = √(r² + h²), since the radius, height, and slant height form a right triangle inside the cone. The lateral (curved) surface area is πrl, and adding the circular base area πr² gives the total surface area, πr² + πrl.
Inputs and what they mean
Enter the base radius (r) — the distance from the center of the circular base to its edge — and the height (h), the straight vertical distance from the base to the apex. Both must be positive numbers in the same unit; the calculator does not convert between units for you, so pick inches, feet, centimeters, or meters up front and use it consistently. The radius has the largest effect on both volume and surface area, since it's squared in every formula.
Limits and edge cases
This calculator assumes a right circular cone — the apex sits directly above the center of the base. An oblique cone, where the apex is off to one side, has a different (more complex) surface-area formula, though the volume formula V = ⅓πr²h still applies as long as h is the perpendicular height. For a frustum (a cone with the tip sliced off), use a dedicated frustum calculator instead, since this tool assumes the cone comes to a single point.