Question about timing of my tourist visa

I believe that Canadians are on the same visa schedule as Americans - 180 days permitted in every 365, so this answer is based on that.  If you're on the same plan that many Europeans are - 90 days in every 180 - the answer will be different.

On your day of arrival, the Polícia Federal system will look back on the previous 365 days, and count the number of days you spent in-country, counting your days of departure and arrival as full days.  The number of days that you have available  is 180 minus that number.

No time you spent in Brazil more than 365 days before your next arrival counts against you.

Thank you. I believe that you are correct that the Canadian and US tourist visa follow the same rules. OK, so if I understand the logic, that means after you are in Brazil for a full 180 days and depart,  you have to wait a full 365 days before you can return. Is that correct? Because, my understanding was that I could return after 180 days, and stay for another 180 days. In other words, 180 days in the country, and 180 days out of the country before you can return.

No, because it's a rolling 365 days.

Let's say that a person arrived on July 5, 2018, and departed on December 31, 2018.  That's 180 days, counting arrival and departure days, as the regulations do. 

The earliest that that person could return would be August 1, 2019, but she could only stay 27 days, because the month of July 2018, and the 27 days she was here in July, would have dropped out of the calculation for her.  If she waits until September 1, another month drops off, and she gets another 31 days.  She keeps getting more days each month that she waits to return until January 1, 2020, when her entire 2018 stay has dropped off her record, and she has 180 days available again.

When business people who travel frequently to Brazil talk about "counting their days", this is what they mean:  keeping track of the days they've used that drop off the back end, and become available again at the front end.  In principle, it's possible to spend alternate months in Brazil indefinitely, as long as you allow for the fact that months have different numbers of days, so arriving and departing on the same day every month could eventually cause a problem.

Ok, that's completely different than what I had understood, I'm embarrassed to say. In my situation, I arrived in Brazil last year on December 29, 2018, and departed May 27, 2019, so I was in Brazil for a total of 149 days.

So I understand that given that I was not there the full 180 days, I could return whenever I want for another 31 days.

But I still don't understand, how do I calculate when I could return and have a full 180 days again. Could you help me with that?

It's confusing, and I doubt that most people at the Polícia Federal do more than read back what the computer tells them.

Taking your numbers as presented, my guess (an educated guess, but still a guess!) would be that you'll have the full 180 days available to you again if you return on or after May 28, 2020 (I'd probably wait until June 1, just to be safe.)  That's when the 27 days you spent in Brazil in May 2019 drop off your record, and you'll be showing no time spent in Brazil during the 365 days prior to your arrival. 

But as you say, you already have 31 days available to you.  On January 1, you'll get three more, as Dec. 29, 30, and 31, 2018 drop off your record.  On February 1, if you're still outside Brazil, you'll get 31 more as January 2019 disappears, and so on, until your record is clear again at the end of May.