Hi,
Another interesting method is to apply a voltage to the primary or maybe even the secondary at the LOWEST desired frequency of operation and look for flat topping. When the flat topping starts to occur, the transformer voltage shouldnt go any higher in voltage than about 80 percent of that no matter what the wattage is. Now we know the voltage.
Looking at the primary (or secondary) wire gauge, we can estimate the max current using 500 or 600 circular mils per amp. Now we know the current.
Power is current times voltage, so we would know the max power the primary (or secondary) can handle and that tells us the power rating of the transformer.
This should work because the designer of a transformer would not want to use a wire gauge that is too much thicker than really required.
Note that the voltage test has to be done at the lowest DESIRED frequency of operation. This means even if the transformer was designed for 50Hz if we want to use it at 25Hz we have to test it at that frequency. This is because the max voltage is related to the max flux density which is related to the core cross sectional area, and that also relates to the frequency of operation.
This also means that we might get more out of it if we run it at a higher frequency as long as the core loss doesnt go up too much.
The window area is related to the power because we can only fit a certain amount of copper inside the window no matter how many turns we have.