Cone development

Calculator of right circular cone / truncated right circular cone development

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Created: 2014-08-23 20:51:02, Last updated: 2020-12-11 13:47:47

The calculator computes parameters of a right circular cone or truncated right circular cone development. The picture below illustrates the task.


We have the lower base radius, radius of the upper base (in case of a truncated cone), and cone height. We need to find the length of the lateral side (or slant height), the lower arc radius, the radius of the upper arc (again, in case of a truncated cone), and the common central angle.

Slant height can be found using Pythagoras.
L = \sqrt{ (r_2 - r_1)^2 + H^2 },
for the full cone r1 is zero.

Radius of the upper arc can be found using triangles similarity.
and for the full cone it is zero.

The radius of the lower arc thus
and for the full cone, it equals L

And central angle

PLANETCALC, Cone development

Cone development

Second base radius (in case of frustum - truncated cone)
Digits after the decimal point: 2
Slant height
Lower arc radius
Upper arc radius
Central angle
Lower arc length
Upper arc length
Length of lower arc chord

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PLANETCALC, Cone development