I am a US citizen who is dating a UK citizen. My boyfriend attended flight school but after finishing, he moved back to the UK. I have visited the UK 3 times since he moved in January. The first time I went for a week, 10 days my second trip, and 3 weeks over summer. I have my 4th trip booked where we are also visiting other countries. I am nervous about getting denied at the UK border. I am not working in the UK, just strictly there to see my boyfriend. I have read that I am allowed there 90 out of 180 days but I'm not understanding when the 180 days starts over. Also, is there a visa I could apply for that fits my situation? I'd love to be able to keep visiting but I know I can only pull that off so many times. Any advice will be highly appreciated! Thanks in advance.
The 90/180 rule applies in the Schengen area, not the UK.
For the UK, you're normally admitted for six months per visit. The immigration officer who decides whether to admit you is supposed to refuse entry if he or she finds that you are not a genuine visitor. One thing that can lead to that conclusion is a finding that you are using frequent visits to live in the UK.
The pattern you have described does not seem close to raising such a concern. You've been in the UK for less than a month and a half over the course of six to eight months.
Another possible concern would be that you intend to stay in the UK to live with your boyfriend. Having a job and a place to live in the US will go a long way toward dispelling such a concern if it ever comes up, but your history of short visits may also work in your favor.