An ordinary FM transmitter transmits from 88MHz to 108MHz. Its coil is about 100nH with 5 to 9 turns of wire on a 3mm inside diameter former. But this circuit uses a lower value coil so its turns are fewer and its frequency is much higher. Do you have a radio that will receive it?
It calculates as 277MHz. My guess is that a factor of 10 is error is hiding there somewhere (because 277/sqrt(10) ≈ 88)
This very simple circuit will have problems:
1) There is nothing to tune its frequency. Usually C1 is a trimmer capacitor.
Often in the really cheap circuits, the inductor is squeezed or stretched to change the frequency. My guess is that the original circuit had an inductance about 10x what is shown here and the dimensions would be more similar to what you suggest (and indeed, that is what I was expecting). In that case, the closely wound coil would give you the bottom of the band, and stretching it out would move you up the band.
2) Its tuned circuit connects directly to the antenna so the frequency will change if anything moves towards or away from the antenna which changes the tuning capacitance.
In fairness, the circuit suggests there is a buffer between the tuned circuit and the antenna.
3) Its frequency will change as the battery voltage runs down because it is missing a voltage regulator.
4) It will sound bad (muffled) because it is missing pre-emphasis.[/QUOTE]