Reviewed by CalcMulti Editorial Team·Last updated: ·← Geometry Hub
A cone is a 3D shape with a circular base that tapers to a point (apex). Its volume is exactly one-third of a cylinder with the same base and height: V = (1/3)πr²h. This 1/3 factor arises from the way the shape tapers — it holds one-third as much as the enclosing cylinder.
The slant height l of a cone (the distance from the apex to the base edge along the surface) is l = √(r² + h²) by the Pythagorean theorem. It differs from the vertical height h.
Lateral surface area (the slanted cone surface, no base) = πrl. Total surface area (including the base) = πrl + πr² = πr(l + r).
V = (1/3) × π × r² × h
V = πr²h — the shape that contains the cone
Sphere Volume CalculatorV = (4/3)πr³ — volume and surface area
Rectangular Prism VolumeV = l×w×h — box volume
Triangle Area Calculator½bh — 2D base of a cone's cross-section
Surface Area CalculatorAll 3D shapes in one calculator
Right Triangle CalculatorPythagorean theorem — used to find slant height
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.