Cone Volume Calculator

Volume equals one third times pi times the radius squared times the height. With radius 3 and height 4 that is one third of pi times 9 times 4, which comes to 37.699112 cubic units.

The slant height is the straight distance from a point on the base rim up to the apex, measured along the surface. It equals the square root of the radius squared plus the height squared, so a radius of 3 and height of 4 give a slant of exactly 5.

Lateral area is only the curved cone wall, found as pi times the radius times the slant height. Total surface area adds the circular base on top, which equals pi times the radius times the radius plus the slant height.

A cone and a cylinder that share the same base radius and height have volumes in a fixed 1 to 3 ratio, a result that follows from integrating the shrinking circular cross sections. That is why the volume formula carries the one third factor.

No. You supply only the radius and the vertical height, and the tool derives the slant height, the lateral area and the total surface area from them automatically.

It is unit agnostic. Enter the radius and height in the same unit, whether centimetres or inches, and the volume comes out in cubic units while the areas come out in square units.

Each value is rounded to six decimal places, and pi uses the full double precision constant. That is accurate enough for schoolwork, engineering estimates and 3D printing checks alike.

Both fields accept values from just above zero up to 1000, in steps of 0.1. Entering zero or a negative number is rejected because a cone must have positive dimensions.

No. It models a right circular cone with the apex directly above the centre of the base. A truncated cone, or frustum, needs both a top and a bottom radius and a different formula.