What power amp is needed for 1800 watt sub?

You didn't mention if that 1800W is Peak or RMS - I'll assume it's RMS.
(In case you don't know the difference: RMS is basically the power level it can handle all the time. Peak is the power level it can handle for a short period of time before damage potentially occurs. Usually, Peak is double the RMS rating.)

Many installers are comfortable recommending a 1 to 1 ratio. So, your 1800W sub would need an 1800W amp.

I don't feel that gives enough of a safety margin. I prefer a 1 to 1.3 ratio. In which case your 1800W sub would need a 2400W amp.