Conical Frustum Calculator

What is a Conical Frustum?

A conical frustum is a three-dimensional geometric shape that results from cutting off the top of a right circular cone with a cut parallel to the base. It is essentially a truncated cone with two circular faces: a smaller top circle (radius r1) and a larger bottom circle (radius r2), connected by a lateral curved surface.

Conical frustums appear frequently in everyday objects such as buckets, lampshades, flower pots, drinking cups, traffic cones with flat tops, and various industrial components like funnels and pipe reducers. The shape combines the structural benefits of a cone with a practical flat top surface. When the top radius equals the bottom radius, the frustum becomes a cylinder.

Formulas and Calculations

The key formulas for a conical frustum are:

Slant Height (s): s = √((r1 - r2)² + h²)

The slant height is the distance along the lateral surface from the top edge to the bottom edge.

Volume (V): V = (1/3)πh(r1² + r2² + r1·r2)

The volume formula combines the areas of both circular faces and their geometric mean.

Lateral Surface Area (L): L = π(r1 + r2)s

This is the area of the curved surface connecting the top and bottom circles.

Top Surface Area (T): T = πr1²

This is the area of the smaller top circular face.

Base Surface Area (B): B = πr2²

This is the area of the larger bottom circular face.

Total Surface Area (A): A = T + B + L

The total surface area is the sum of all exposed surfaces: top, base, and lateral.

How to Use the Conical Frustum Calculator

Using this calculator is simple. Enter the top radius (r1), bottom radius (r2), and height (h) of the frustum. The tool will instantly compute the slant height, volume, lateral surface area, top surface area, base surface area, and total surface area. All calculations are performed in real-time in your browser.

All values must be positive numbers. The top radius (r1) should be smaller than or equal to the bottom radius (r2) for a standard frustum.