Cone Volume & Surface Area Calculator

About this calculator

A right circular cone's volume is exactly one-third that of a cylinder with the same base and height — volume = (1/3)πr²h — a relationship first proven geometrically by Eudoxus and later by Archimedes. Its total surface area combines the flat circular base, πr², with the curved lateral surface, πrl, where l is the slant height found from the Pythagorean relationship l = √(r² + h²).

These formulas are essential wherever cone-shaped containers or structures need to be sized or manufactured: ice cream cones, paper filter cones, traffic cones, funnels, and conical grain silos or hoppers all rely on the volume formula to determine capacity, and the surface area formula to calculate how much material is needed to build them. Civil and mechanical engineers also use cone volume when calculating the capacity of conical tanks and the material needed for conical roofs on silos and towers.

This calculator takes a cone's radius and height and returns both its volume and total surface area.