I’ve bought a spinning bike that has the cage pedals. I have cleat shoes which I prefer to ride in, so I bought some cleat pedals to fit to the spinning bike. Trouble is I've just taken the existing pedals off, and the thread is way bigger on the spinner pedal than the one I have on the pedals I have bought. Is there a bigger pedal or adapter available?
Almost all adult bikes have 9/16" threads, with 20 TPI. One side is left-hand thread.
The other standard option is 1/2" thread which is intended for children's bikes.
There are rare vintage standards around 10 and 12mm but your spin bike wouldn't have these.
Finally there's a chance your spin bike has some proprietary pedal thread. Do you have access to calipers?
While pedal adapters do exist from 1/2" to 9/16" they are not cheap, and they separate your feet by some, also known as "increasing the Q factor"