Cone Volume Calculator

Formula

V = πr²h/3

Worked example

With Radius: 5 units, Height: 4 units, volume is 104.719755 cubic units.

Calculation method

The rule is V = πr²h/3.

For this cone volume example, changing radius from 5 units to 6 units while keeping the other inputs fixed changes volume from 104.719755 cubic units to 150.796447 cubic units.

Reading volume

The result uses cubic units. Scaling every length by a factor of two multiplies volume by eight. A cone has one circular base and tapers to a point; its radius is measured at that base. In the worked values on this page, radius 5 units, height 4 units produce volume 104.719755 cubic units.

Practical use

Use the formula for an idealized cube, prism, cylinder, cone, sphere, or hemisphere as named. This model suits a pointed solid, funnel, or conical covering when the cross-section narrows toward an apex.

Limits and common mistakes

Use consistent length units, and distinguish radius from diameter. A real container’s usable capacity can differ from its idealized geometric volume. The slant height differs from perpendicular height; total surface area and lateral area use them differently.

Why the relationship works

Volume measures occupied three-dimensional space. Prisms multiply a base area by height, a cone uses one third of the matching cylinder volume, and sphere-based formulas depend on radius cubed. A radius is half the diameter; using the diameter as if it were radius can greatly overstate volume. The cone volume rule uses radius (units), height (units) in V = πr²h/3; read each symbol as the field named on this page.

Interpreting another set of values

For cone volume, the fields labeled radius (units), height (units) are the known quantities. The calculator solves for volume in cubic units using V = πr²h/3. The output is the ideal solid’s occupied space, so the unit is cubic. It does not include wall thickness or material outside the modeled boundary. When comparing two calculations, keep their units and input definitions identical.

For a second cone volume check, keep the other default inputs fixed and change radius from 5 units to 7 units. Volume changes from 104.719755 cubic units to 205.25072 cubic units. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

Keep every entered dimension in the same length unit before calculation. Volume uses cubic units, surface area uses square units, and a solved radius or side uses a linear unit. Real containers may have wall thickness, open ends, rounded edges, or tapered shapes that the ideal solid formula does not include. The reported volume is a volume. If the input lengths were centimeters, its unit would be cubic centimeters; the numerical 104.719755 cubic units describes occupied space rather than an outer covering.