oi couldn't figure the easier way for determining selfinductivity if you already have em. coil, so here it is :
we need basic three values about coil, it's current, voltage, and resistance. i believe you already know voltage, so you can measure the resistance of coil with normal ohmmeter, and then get current with I = U / R.
we need to know number of turns too. use the formula R = ro * (l/S), where ro is specific resistance (you can find those values on the internet for every material, for copper is 0,0175), l is length of wire and s is surface (in mm2). then you can use simple geometry to determine number of turns. you need to know the surface value for that. N = lair / 2*sqrt(S/3.14). lair is length of coil, not of wire, and you can use normal meter to measure it.
in my previous post i gave that formula. Us is selfinductivity, and L is inductivity. Us is voltage that appears when magnetic flux changes inside the coil as direct effect of current change trough coil. so we need to know inductivity to determine selfinductivity.
Us = -L*(dI/dt)
inductivity : L = N^2 / Rm . we already calculated number of turns so onlything that's left is Rm, the electromagnetic resistance.
Rm = theta / fi
theta = I * N , the magnetomotoric force. we have both of values required, the current trough coil and number of turns
fi = B * S, the magnetic flux. note that S here isn't same as surface of the wire, it's the surface of electromagnetic pole. you can determine it by measuring the radius of the coil, and then using r^2*pi.
B = [mi-zero]*[mi-relative]*(I*N)/l , the field strenght. [mi-zero] is permeability of free space constant, and it equals 1,257e-6 (0,000001257). [mi-relative] is permeability of core. if your coil doesn't have iron or other core beneath it, then youre using air coil, and [mi-relative] is 1. for other materials refer to this URL : http://www.oz.net/~coilgun/theory/materials.htm.