Frustum Volume Calculator (Conical)

Calculate the volume of a conical frustum, including liquid capacity. Many pottery mugs are frustum shaped (more below).

Use for top radius

Use for bottom radius

Applies to all dimensions above

Frustum Volume Calculator FYIs...

To calculate, enter the height of the frustum, measured from top to bottom; And, the frustum's top radius, as well as its bottom radius. Radius is half the diameter.

What is a Conical Frustum?

A conical frustum is a cone which is not pointed at the top; instead, it is the shape that remains after the top portion of a cone is removed, having been bisected by a flat parallel plane (real or imagined). For this reason, it is also referred to as a truncated cone.

By design, many hand made pottery mugs and cups are frustum shaped and not cylinders; that is, the radius of the top and bottom often differ, and there is a slight angle to the side. A terracotta flower pot, adorning many a patio, is a frustum, albeit inverted.

Truncated Cone Frustum Volume Calculation

Volume is the liquid capacity of the frustum shaped object. For example, if it's a pottery mug or teacup, it's the amount of liquid it can hold. The formula to calcuate the volume of a cylinder is:

Volume = 1/3πh(r12+r1r2+r22)

where r1 is top radius, r2 is bottom radius, h is the height, and π (pi) is approximately 3.14

The result of calculating the frustum's volume is in cubic inches (or centimeters). Using the volume, the liquid capacity of the conical frustum is calculated in several common metrics (pints, cups, liters, etc.)

Note that liquid capacity will be slightly larger than the frustum shape can actually hold unless you measure from the inside walls of the frustum's top and base; Otherwise, the wall's thickness is included in the calculation.