1800 watts on a 120v = 15 amps. If anything else is on, that would trip a 15amp breaker. That is the most common size for bedrooms, dining rooms etc.

I would only use the device on 20 amp circuits in GFCI protected recepticles.

This cooktop is a 120 volt model? Plug-in 120V heating appliances >1500 watts are unusual, but not unheard of. Some hair dryers and toasters are 1800+ watts, but these are typically used for just a few minutes at a time. I would not use this cooktop for long periods on a 15A circuit, even if there is nothing else on the circuit. Of course, if there are multiple heating elements, and you're not using them all, you should be OK on a 15A circuit even of it's used for an extended period.
Check the manual to see if a 20A circuit is required. If so, I'd expect the cooktop to have a 20A plug on the cord. I guess this would depend on whether the unit is designed for "continuous use."

1800watts is a rating. The device probably will never actually draw that much. If it comes with a 15 amp cord and plug then it is designed to be used on a regular cirucit. I would not be using anything alse on the circuit at the time.

Thanks for the info!