Cone Calculator
Calculate the volume, surface area, and slant height of a cone from its radius and height.
How it works
- 1Enter the cone’s base radius and vertical height.
- 2Read the volume ((1/3)π r² h), surface area, and slant height.
- 3Slant height is √(r² + h²); surface area is π r (r + slant).
Use cases
- Find the capacity of a conical container or hopper.
- Estimate material for a cone, funnel, or party hat.
- Check geometry homework on cones.
Frequently asked questions
What is the volume of a cone?
Volume = (1/3) × π × radius² × height — exactly one third of a cylinder with the same base and height. Radius 3, height 4 give about 37.70 cubic units.
What is slant height?
The distance from the base edge to the apex along the surface: slant = √(radius² + height²). For radius 3 and height 4 it is 5.
What is the total surface area?
The base plus the curved side: π r² + π r × slant = π r (r + slant). Radius 3, height 4 give about 75.40 square units.
Related tools
See all →Calculate the area and perimeter of a rectangle from its width and height, with a labeled diagram.
Calculate the area and circumference of a circle from its radius, with a labeled diagram.
Calculate the area (Heron’s formula) and perimeter of a triangle from its three sides.
Calculate the area and perimeter of a trapezoid from its two parallel sides, height, and legs.