Cone
A right circular cone narrows from a circular base to a single apex directly above the center. Its volume is one third of a cylinder with the same base and height.
Give your shape a size.
Use the same unit for every dimension. Changing the unit relabels the measurements; it does not convert them.
From dimensions to an answer
Know its properties
| Flat faces | 1 circular base |
| Apex | 1 |
| Slant height | ℓ = √(r² + h²) |
| Axial cross-section | An isosceles triangle |
Useful formulas
Volume: V = πr²h / 3
Total surface area: S = πr(r + ℓ)
Lateral area: L = πrℓ
Cone: common questions
Wondering about the why? Start here.
Why is cone volume one third of cylinder volume?
A cone has one third the volume of a cylinder with the same base area and perpendicular height. Their formulas are πr²h/3 and πr²h respectively. The comparison only applies when both radius and height match.
Compare with a cylinderHow do perpendicular height and slant height differ?
Perpendicular height runs from the tip straight down to the base plane. Slant height runs along the cone’s side. For a right circular cone, slant height is √(r² + h²). This calculator accepts perpendicular height and derives slant height for surface area.
See the Pythagorean connection