Cone Calculator

Formula

How this is calculated

This tool models a right circular cone — one whose apex sits directly above the center of a circular base. You supply two measurements in the same unit: the base radius r (half the width of the circular bottom) and the perpendicular height h (the straight vertical distance from base to apex). Every result is derived purely from these two numbers.

Volume uses 1⁄3 × π × r² × h. The term π × r² is the area of the circular base, multiplied by height gives a cylinder, and the 1⁄3 factor reflects that a cone fills exactly one third of that cylinder. The slant height — the diagonal distance from apex to base edge along the surface — comes from the Pythagorean theorem, √(r² + h²), since r and h form the legs of a right triangle. Total surface area, π × r × (r + slant), adds the flat base (π × r²) to the curved lateral surface (π × r × slant).

Inputs must be positive; zero or negative values return no result. Lengths use whatever single unit you choose, volume comes out in that unit cubed, and area in that unit squared. Results are rounded to four decimals, so values involving π or irrational slant heights are approximate.

Examples