Conical Frustum Volume Calculator

A conical frustum is what is left when the pointed tip of a cone is sliced off by a plane parallel to its base. It has two parallel circular ends, a wider bottom and a narrower top, joined by a slanted side. Buckets, lampshades and drinking cups are everyday frustums.

Volume equals one third times pi times the height times the quantity bottom radius squared plus bottom radius times top radius plus top radius squared. Writing rb and rt for the radii and h for the height, that is (1/3) pi h (rb squared + rb rt + rt squared).

The slant height is the square root of the height squared plus the square of the difference between the two radii, or sqrt(h squared + (rb - rt) squared). It measures the sloped distance along the outside from the bottom edge to the top edge, not the vertical height.

Total surface area adds the slanted lateral band to both flat circular ends. It equals the lateral area plus pi times the bottom radius squared plus pi times the top radius squared, so it treats the frustum as a solid capped at both ends.

Lateral area is only the curved slanted side, with no ends included. It equals pi times the sum of the two radii times the slant height. This is the figure you want for the material in a lampshade or a cone-shaped skirt that is open top and bottom.

The tool is unit agnostic. Enter all three lengths in the same unit and the volume comes out in that unit cubed while both areas come out in that unit squared. Feed it centimeters and you get cubic centimeters and square centimeters.

Yes. When the bottom and top radii match, the shape is a cylinder. The volume formula collapses to pi times the radius squared times the height, the slant height equals the plain height, and the calculator reflects that, as the 3, 3, height 5 example shows.

All three inputs must be strictly greater than zero. A zero top radius would make a full pointed cone rather than a frustum, and a zero bottom radius or height would collapse the solid, so the tool shows a warning instead of a misleading result.

Calculations use full double precision internally and each output is rounded to six decimal places. Trailing zeros are dropped when displayed, which is why an exact answer like a slant height of 5 shows without decimals.

Yes. The entire calculation runs locally in your browser with JavaScript. No radius, height or result is ever sent to a server, so you can use it offline once the page has loaded.