Cone Volume Calculator

V = (1/3)πr²h. One-third of the cylinder of same base and height.

Inputs

Result

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General calculation reads

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How to use this calculator

  • Enter radius and height.
  • Read volume, slant height, surface area.

About this calculator

A cone is a cylinder with one end pinched to a point. Volume = (1/3) × base area × height = (1/3)πr²h — exactly one-third of the corresponding cylinder. Slant height = √(r² + h²) is the distance from apex to base edge. Lateral surface = πr × slant. Used in ice cream cones, party hats, traffic cones, and conical roofs.

Frequently asked

Why one-third?+
A pyramid (or cone) on the same base and height has 1/3 the volume of a prism (cylinder). Provable via calculus or Cavalieri's principle.
Slant height vs. height?+
Height: perpendicular from apex to base center. Slant: from apex along the side to base edge. Slant > height.
Truncated cone?+
Frustum — cone with top cut off. Volume = (1/3)πh(R² + Rr + r²). More complex but useful for buckets, drinking cups.
Surface area total?+
Lateral (πr × slant) + base circle (πr²). For an open-top cone: just the lateral.
Real-world cone?+
Traffic cones, ice cream, party hats, paper cups, the lower part of a tornado, conical mountain peaks.

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