Cone & Frustum Volume Calculator

Conical Geometry & Formulas

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (typically circular) to an apex point.

Mathematical Definitions

1. Right Circular Cone Volume (V): V = (1/3) × π × r² × h

2. Slant Height (s): s = √(r² + h²)

3. Lateral Surface Area (A_L): A_L = π × r × s = π × r × √(r² + h²)

4. Total Surface Area (A_T): A_T = π × r × s + π × r² = π × r × (s + r)

Storage funnel – calculation example

Let’s calculate the holding capacity of a conical feed hopper with base radius 3 ft and vertical height 6 ft:

1. Base radius: radius = 3 ft.
2. Vertical height: height = 6 ft.
3. Slant height: slant height = 6.71 ft.
4. The calculation results are available for you: hopper volume = 56.55 cu ft (423.0 US gallons / 1.60 m³).
5. Lateral surface area: lateral area = 63.22 sq ft.

💡 A cone occupies exactly one-third the volume of a cylinder that shares the same base diameter and vertical height.

Truncated Cone (Conical Frustum)

When a cone is sliced horizontally by a plane parallel to its base (common in buckets, lampshades, and chemical hoppers):

V = (1/3) × π × h × (r₁² + r₁ × r₂ + r₂²)

Where r₁ is the bottom radius, r₂ is the top radius, and h is the vertical height between the two circular faces.