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Volume of a Cone Calculator

Interactive 3D cone — adjust dimensions, see volume update live

Calculate the volume of a cone instantly with this free interactive 3D calculator. The formula is V = (1/3)πr²h, where r is the radius of the circular base and h is the perpendicular height. A cone has exactly one-third the volume of a cylinder with the same base and height. Enter your values in the panel and watch the 3D model update in real time.

Use this tool for real-world calculations: find the volume of ice cream cones, funnels, party hats, conical storage tanks, or piles of sand and gravel. For example, a cone with radius 3 cm and height 8 cm has a volume of approximately 75.4 cm³. The calculator also shows the slant height and surface area.

Need help with the math? The built-in AI chat assistant can explain why the 1/3 factor appears, walk through related rates problems, or help you convert between units.

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FAQ

What is the volume of a cone?
V = (1/3)πr²h, where r is the base radius and h is the height.
What is the surface area of a cone?
SA = πr² + πrl, where l = √(r²+h²) is the slant height.
Why is a cone one-third of a cylinder?
A cone with the same base and height as a cylinder has exactly one-third the volume. This can be proven by calculus (integrating circular cross-sections) or by Cavalieri’s principle.
How do I use this cone volume calculator?
Enter the base radius and height in the input panel. The 3D model updates live as you adjust the values. Volume, surface area, and slant height are computed instantly. You can also ask the AI chat assistant for step-by-step explanations or help with related problems.
What are real-world uses for cone volume?
Calculating ice cream cone capacity, funnel volume for liquid flow, party hat material estimation, conical tank capacity (water treatment, agriculture), and pile volume for sand, gravel, or grain. The formula V = (1/3)πr²h applies to any right circular cone.

Related Topics

Cone Net GeneratorCylinder Volume Calculator