I have a toroidal ferrite core which has an outer diameter of 15 cm, inner diameter of 11 cm and height of 4 cm. I want to use it to make a transformer which takes in mains voltage (240V) and outputs high current (>50A) at any voltage (even half a volt will be okay). I will be using wire of 2.5 square millimeters for winding the primary and secondary of 10 square millimeters. How many turns of each do I need to make? Will this be safe? Is there anything else I need to know?
Any transformer connected to 240V AC has to have sufficient inductance in the primary so that it isn't taking a large magnetization current - just think of the primary and ignore the secondary for now - imagine you are only making an inductor to connect to the AC - you don't want it taking ten amps just by itself.
Of course there is a technical reason for not taking ten amps - this will almost certainly saturate the core and fry.
So, armed with the details you have on the toroid such as the \$A_L\$ value, this will help you understand how many turns are needed to obtain an inductance of (say) 10 henries. 10 henries will have an impedance of about 3000 ohms at 50Hz and will take a current of about 80mA when connected to the 240V AC.
Then you need to decide if this will saturate the core and fry. You Used \$A_L\$ and a target inductance of 10 henries to tell you how many turns you need to wind then, you can calculate the magneto-motive force (ampere-turns). Then, divide MMF by the net length around your toriod to get H (magnetic field strength, ampere-turns per metre) and you are nearly there.
Referring to the BH curve in the toroid's data sheet and using the value of H just calculated determine what magnetic flux density (B) you will be getting from the graphs normally supplied - if it's more than about 0.4 Teslas then you will likely run into saturation problems.
I'm not doing the math but it's going to be a close run thing as to whether this toroid is big enough to tolerate mains voltage across the primary - ferrite toroids are not normally used as regular AC transformers - they are better suited to a much higher frequency (as per what you get in an off-line switcher) because of this issue.
If you don't know what the ferrite is made of forget it (and I mean that).
Winding the secondary is a cinch in comparison but before any advise is given, technical detail of the toroid material is needed.