Connecting 3 wire cooktop to home 3 wire 240v

Their wiring is based on a 240V/120V circuit with hot/hot/neutral/ground, which is typically black/red/white/green-or-bare. Normally white = neutral. However, if you have a pure 240V circuit wired with cable (as opposed to individual wires in conduit), it is perfectly legitimate for it to be hot/hot/ground using black/white/green-or-bare. So you should be just fine.

If you want to be 100% sure, use a multitester to check the voltage between the house wires. You should have ~240V black to white and ~120V black to bare and white to bare, and if so then you are all set. However, if you have ~120V black to white, ~120V black to bare and ~0V white to bare then you actually have a 120V circuit, which will not work for your cooktop.

Important: Be sure to compare the existing breaker with the requirements for the new cooktop. Typical is 30A, but it can be different. If the new cooktop matches the existing breaker then you are all set. If the new cooktop requires a smaller circuit then you can simply replace the breaker. However, if the new cooktop requires a larger circuit then before replacing the breaker you have to determine whether the wires are large enough to handle the current.

If that is indeed a 240V circuit, the white wire kinda shoulda been re-marked with tape to indicate that it is a hot wire. Prior to about 20 years ago, they were allowed to skip the marking "if the usage was obvious". The reason for the change is that their "obvious" is not your "obvious".

If you are confident that it is indeed 240V, remark that white wire with black or colored electrical tape. (red is perfectly fine).

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Code does not require you to mark different kinds of hot by their function... any hot can be any color not reserved for other things. *

White and gray are reserved for neutral.

Green, yellow w/green stripe, and bare are reserved for safety ground.

* with an extremely obscure exception relating to 3-phase power, that isn't even worth mentioning.