# The number of circles that will fit inside the area of larger circle?

Let's say circle $\omega_1$ has a diameter $X$. Let $X>Y$; $Y\in \mathbf{R}^{+}$. How many circles with diameter $Y$ will fit inside $\omega_1$?

Is there a formula for this?

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– Alex Wertheim Aug 16 '13 at 1:52
You can assume $Y=1$ without loss of generality. – MJD Aug 16 '13 at 2:08
Given that many circle packing methods are conjectured (but not proven) optimal, the answer to your question "is there a formula for this" would be no. – hasnohat Aug 16 '13 at 13:01
you can $\frac{(x-x\%y)}{y}$ with the area. – user52413 Aug 28 '13 at 8:52

$${{\pi {X^2}} \over {\pi {Y^2}}}$$
=$${{{X^2}} \over {{Y^2}}}$$
This only gives an upper bound for the number of circles of diameter $Y$ which fit into a circle of diameter $X$. However, that upper bound is not attainable (unless $X = Y$). For instance, try packing $4$ circles of diameter $1$ into a larger circle of diameter $2$. You will see that it is not possible. – JimmyK4542 Oct 6 '14 at 0:44