Number of Circles in a Circle

This is a simple online calculator to calculate the number of circles that could be drawn inside a larger circle. Imagine an 'Idly' plate, the cooking utensil to make the South Indian food Idly, which is the perfect example for this scenario. There will be a large outer circle and a number of inner circles. More technically it can be described as a symmetric ring of n circles in which adjacent circles are tangent and you could circumscribe a larger circle around the ring.

Inner Circular Ring Calculator

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Formula:

n = (π * R2) / ( 2 * r)2 Where, r = Diameter of Inner Circle R = Diameter of Outer Circle n = Number of Circles in Inner Ring
Number of Circles in a Circle

Example:

Diameter of the exterior circle is 10 cm and diameter of the inner circular rings is 3cm, calculate the number of inner circles in the larger circle.

Solution

n = (π * R2) / ( 2 * r)2
= 3.14 x 102 / 62
= 314 / 36
= 8.7222
= 8

This kind of inner circular ring arrangement is used in geometric designs. The diameter of the outer circle depends on the number and diameter of inner circles. Note that all the circles inside the ring have an even diameter. It can be stated that the number of inner circles depend on the diameter of the outer circle and inner circles.

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