Cone Volume Calculator
A cone is a three-dimensional shape with a circular base that tapers smoothly to a single point called the apex or vertex. The volume of a cone is exactly one-third the volume of a cylinder with the same base radius and height, expressed as V = (1/3) * π * r² * h. The height is the perpendicular distance from the base to the apex, not to be confused with the slant height, which is the distance along the sloped surface from the apex to the edge of the base. The slant height is found using the Pythagorean theorem: l = sqrt(r² + h²). The lateral surface area is the curved side only and equals π * r * l. The total surface area includes both the lateral surface and the circular base, calculated as π * r * (r + l). This calculator computes the volume, slant height, and both lateral and total surface areas from the radius and height. Enter both values in the same unit of measurement.
Cone volume formulas
Volume = (1/3) * π * r² * h
Slant Height = √(r² + h²)
Lateral Surface Area = π * r * l
Total Surface Area = π * r * (r + l)
Reference volumes
| Radius | Height | Slant Height | Volume |
|---|---|---|---|
| 2 cm | 5 cm | 5.39 cm | 20.94 cm³ |
| 5 cm | 10 cm | 11.18 cm | 261.80 cm³ |
| 10 cm | 15 cm | 18.03 cm | 1,570.80 cm³ |
| 1 m | 2 m | 2.24 m | 2.09 m³ |
| 3 m | 7 m | 7.62 m | 65.97 m³ |
Cone volume calculator: frequently asked questions
What is the formula for cone volume?
The volume of a cone is V = (1/3) * π * r² * h, where r is the radius of the circular base and h is the height. The factor of 1/3 shows that a cone with the same base and height as a cylinder holds exactly one-third the volume of that cylinder.
What is slant height?
Slant height is the distance along the sloped surface from the apex (point) of the cone to the edge of the base. It is calculated using the Pythagorean theorem: l = sqrt(r² + h²), where r is the radius and h is the height.
What is the lateral surface area of a cone?
The lateral surface area is the curved side surface only, not including the circular base. It is calculated as π * r * l, where r is the radius and l is the slant height.
What is the total surface area of a cone?
The total surface area includes both the curved lateral surface and the circular base. It is calculated as π * r * (r + l), which combines the lateral area (π * r * l) and the base area (π * r²).
What are examples of cones?
Common cones include ice cream cones, traffic cones, party hats, funnels, tornado shapes, drill bits, pine cones, and conical roofs on buildings.
Official sources
- Khan Academy: Volume and surface area of solids.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.