A cone is a solid formed by all rays from one point (the apex) passing through a flat base.
Formula
The volume of a cone is one third of π times the base radius squared times the height ⇒ V = 1/3 * π * R2 * H
Example
A sand pile with a 2 m base radius and 1.5 m height: V = 1/3 × 3.141592 × 2² × 1.5 ≈ 6.28 m³ — a third of a cylinder of the same size.
Units
The volume comes out in cubic units of the dimensions you enter: centimetres give cm³, metres give m³. Use the same unit for all dimensions. Conversion: 1 L = 1 dm³ = 1000 cm³, 1 m³ = 1000 L, 1 mL = 1 cm³.
Good to know
- The height is perpendicular from the apex to the base, not the slant height. From the slant height
L:H = √(L² − R²). - The pile radius is easy to get from the base circumference:
R = C / (2π).
Where it is used
- Piles of sand, gravel, grain, salt.
- Funnels, hoppers, conical roofs, ice-cream cones.
- Material for 3D printing and casting.
How to use
Enter the dimensions (decimals with a dot or comma) and press “Calculate”. You get the formula with your numbers and the result with a copy button, and the 3D model is redrawn to your dimensions.