Knowing the number of turns is a start, but you also need to know the value called Al for the material, so I am guessing a calculation method is not viable here.
Next is using a LCR bridge instrument, which you may not have handy.
Another way is to temporarily put it in series with various capacitors, and connect to the end of a 50 Ohms cable, maybe with a further 100R in series, and use a signal generator. A diode probe (simple rectifier circuit), or maybe an oscilloscope across the inductor-capacitor combination will show a "dip", or collapse in the signal voltage as you cross the resonant frequency.
From there, you can use the formula.. Inductance = 1/(4*(pi^2)*(Freq^2)*Capacitance)
There is a great picture of the arrangement, and the full explanation of RLC resonance in the link ..
HERE -->
LINK https://en.wikipedia.org/wiki/RLC_circuit
The YouTube link suggested by wp100 is excellent. If you have an oscilloscope handy, and can contrive a fast edge logic square-wave to use instead of a signal generator, then measuring the "ringing" frequency is another way to get at it.