Elliptic Cone Frustum Volume Calculator

Find the volume of an elliptic cone frustum from the semi-axes of its bottom and top elliptical faces and its height. Shows both base areas too.

Input

Enter the semi-major and semi-minor axes of the bottom and top faces and the height to compute the volume of an elliptic cone frustum.

Bottom semi-major a1

Bottom semi-minor b1

Top semi-major a2

Top semi-minor b2

Height h

Volume

191.554421

Bottom face area

47.12389

Top face area

18.849556

Use consistent length units. Areas are in squared units and the volume in cubed units.

An elliptic cone frustum is a solid bounded by two parallel similar elliptical faces, generalizing a circular cone frustum to ellipses.
The volume is V=（πh/3）×（a1b1＋a2b2＋√（a1b1a2b2）），where a1,b1 are the bottom semi-axes, a2,b2 the top semi-axes, and h the height.
The bottom face area is π×a1×b1 and the top face area is π×a2×b2.
Use consistent length units. Areas come out in squared units and the volume in cubed units of your input.
As the top face shrinks toward a point it approaches an elliptic cone, and when top and bottom match it approaches an elliptic cylinder.

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