I will assume that each of the small circles that have to touch two other small circles can be touching additional small circles.  I presume what you mean by "needed to fill a circular area" is that the n small circles cannot be made any larger and still fit into the large circle, which is the same as stating that the large circle is as small as possible to contain the n small circles.Since the scales are arbitrary, make 1 be the radius of the small circles and make x be the radius of the large circle that encloses all of the small circles.  Then, you want to know if there is a formula x(n) for n=3, 4, 5, ... in some closed form.  (For n=2, you can't have a small circle touching two other small circles, but in any case that is a trivial solution.)This is known as a packing problem.  Your specific example is Circle packing in a circle.  I don't know that there is a closed form formula for x(n).  Since the packing is optimal (not all of them have been proven to be optimal), it means that, for n circles, the large circle cannot be smaller than radius x.The more general cases are explained by the Wikipedia article Packing problems.