Cone Volume and Surface Area Calculator
Calculate right-cone volume, slant height, and total surface area from positive base radius and perpendicular height.
Calculate cone volume
How this tool works
A right circular cone combines a circular base with an apex directly above its centre. This calculator derives slant height from radius and perpendicular height before reporting both volume and total surface area.
Volume equals πr²h/3. Slant height equals √(r²+h²), and total surface area including the base equals πr(r+slant height).
How to use it
- Enter positive base radius.
- Enter positive perpendicular height.
- Read volume, derived slant height, and total surface area.
Worked examples
Radius four cone
- Input
- Radius 4, height 9
- Output
- Volume approximately 150.80
The circular base area is sixteen π; multiplying by height nine and dividing by three gives forty-eight π cubic units.
Radius three cone
- Input
- Radius 3, height 4
- Output
- Volume approximately 37.70
The three-four-five right triangle gives slant height five, while volume is one third times nine π times four.
Limitations
- The model assumes a perfect right circular cone.
- Thickness, seams, truncation, and manufacturing allowances are not included.