Back in the old days, there used to be a ranking in Google, each website had page rank. Every user used to see the same search results for a given search query and websites were ordered based in several (rather few compared with nowadays) factors, being the most important factor its page rank and the page rank of the websites that linked to its pages.
Today Google's page rank is just one of the thousands factors they use to rank a website and it's pages. Things had evolved to make a personalized user experience. Users will see different search results based in previous searches, language, location, and many more things, some of them can be neutralized with browser's private mode, but there is no general ranking anymore, there is no way to make sure that two different users will see the same results for the same query.
The closest tool to analyze webpages position for search queries objectively is to use the Search Analytics Report in Search console. Then you can see the search queries your site is receiving and their positions in SERP:
Position - The average position of the top most result from your site.
So, for example, if your site has three results at positions 2, 4, and
6, the position is reported as 2. If a second query returned results
at positions 3, 5, and 9, your average position would be (2 + 3)/2 =
2.5. If a row of data has no impressions, the position will be shown as a dash (-), because the position doesn't exist