240V, that's an unfair example. As a low IQ person, I sidestepped trying to actually calculate the heat generated by different resistive wires (has to be above the melting point of styrofoam) and thought linearly about what I wanted to do, which was cut styrofoam, so google styrofoam cutter hot wire, got me to amazon.

Correct answer would have been "I don't know, whats the resistance of the wire".

1.2 Ohms per meter, 45cm (which was what i had) would burst in a flash of liquid metal when connected to 240V.

the correct answer is to cut the styrofoam.

https://www.amazon.com/Foam-Electric-Cutting-Machine-Control...

A form of "Use other people's solutions"

have you ever heard of steam tables?

Do I need to give you a number?

Can I just build something that allows me to control voltage and turn it up until it cuts, then measure?

The low iq solution would be to steadily ramp up the voltage until it cuts.

Hah, apparently I am low IQ but still getting it done.

The voltage in your wall sockets is a given, so the question should be "Which resistive wire do I need to best cut Styrofoam with electricity?"