Without being too specific about what is wrong with the information given so far, I suggest that the problem is more complex than simple formulas will give. An exact formula would be quite difficult, but there is some possibility of a reasonable approximation. Here is some notation:
t=radius of the wire and its insulation
Ri = inner radius of the spool
Ro = outer radius of the spool
First assume that the flanges of the spool are so close together that the wire will look like the way sailors coil rope on the deck of a ship(flat coil). To make such a coil, one would start at the core of the spool (the inner radius Ri) and and make n turns to get to the outer edge of the flange (the outer radius, Ro). Then we can find the number of turns to be
n=(Ro-Ri)/t
The first time around the core requires 2pi(Ri+t) amount of wire, since the radius of the second turn has been increased by t, the second turn will require 2pi(Ro+2t) amount of wire. The last time around will require 2pi(Ri + nt) wire. If all of the turns are added, the formula I get is
Wire on one flat coil = 2n(pi)(Ri + n(n+1)t)
To complete the calculation, you must know how many flat coils are on the spool. If D is the distance between flanges then
m=D/t where m is the number of flat coils.
Therefore, the total length is
Total = m(wire on one flat coil).
Of course, wire does not wrap on a spool exactly like a bunch of flat coils. The second layer on the spool will fall in the space between coils of the first layer, think of three tangent circles. For this and some other reasons, the formula is only an approximation. However, all of the information required can be obtained with a ruler or tape measure.