90/180 rule. Do I have to leave Schengen for 90 consecutive days after the 180 day period (even if I only stayed 90 days in the 180 day period)

The 90/180 rule uses a rolling window. This means, that, on any day you are present in Schengen, if you look at the 180 previous days (or more precisely, the 179 previous days + the current day), there shouldn't be more than 90 days spent in Schengen (even 5 minutes in that day count as a full day, so arrival and departure days are counted).

For the 90/180 rule (there may be other reasons), the only case when you need to spend exactly 90 days outside of Schengen is if you just spent exactly 90 days in Schengen (you are on day 90 of a 90-day stay in Schengen).

For all other cases, you have to check for each day you want to spend in Schengen what was the number of days spent in Schengen in the previous 180 days to determine if you can stay in Schengen or not.

Examples (I'll number days rather than use dates because months with 28/29/30/31 days are confusing).

• You stayed in Schengen from day 1 to day 90: you cannot come back to Schengen before day 181 (and you can say for up to 90 days at that point).
• You stayed in Schengen from day 1 to day 30: you can come back and stay a maximum of 60 days within the period from days 31 to 180.
  • You may be able to stay longer beyond day 180, for instance if you come back on day 121 or later, you can stay for the full 90 days (because on day 181, day 1 will "exit" the rolling window, and so on for the following days).
• You stayed in Schengen from day 1 to day 30, days 61 to 90, days 121 to 150 (every other month, for a total of 90 days): you cannot come back before day 181.
  • If you come back on day 181, you can stay only 30 days, and then you need to wait 30 days before coming back.

You can use the calculator at https://ec.europa.eu/assets/home/visa-calculator/calculator.htm to check things. It's by far not the most user-friendly tool every invented, though!

Not that all of this is in terms of respecting the 90/180 rule for C visas and visa-free travel. There may be other rules which dictate different requirements for various reasons.

Note: this answer does not apply to citizens of Antigua and Barbuda, The Bahamas, Barbados, Brazil, Saint Kitts and Nevis, Mauritius, or Seychelles

After discussing this a bit they agreed that I hadn't stayed over 90 days during that period, but instead that I was required to leave Schengen for a consecutive 90 day period after that 180 day period had completed.

This sounds incorrect. More specifically, it sounds like they are asserting that a 90-day absence is required following any 180-day period in which you spent 90 days in the Schengen area. Here is a counterexample showing that this reformulation of the rule is actually incorrect.

(If you stay in the Schengen zone for 90 consecutive days, you do need to remain away for 90 consecutive days, so whether their statement is correct depends on what they mean by "that 180-day period"; if they mean the 180-day period that started when you entered, they're wrong, but if they mean the one that ended when you left then they're correct.)

• Enter on day 1; depart on day 80; 80 total days of presence.
• Enter on day 171; depart on day 180; 90 total days of presence.

Is entry forbidden until day 270? or until day 271? Let's translate these days numbers into dates and use the Schengen calculator. If day 1 is March 1, 2021, then we have the following:

• April 1st is day 32
• May 1st is day 62
• May 19th is day 80, the day of initial departure
• June 1st is day 93
• July 1st is day 123
• August 1st is day 154
• August 18th is day 171, the day of return
• August 27th is day 180, the day of final departure

Enter these dates into the calculator, and set the "date of entry/control" to August 28th, and what do you get?

The stay may be authorised for up to: 80 day(s)

What? How is this possible?

Well, on August 28th, the day of presence on March 1st no longer counts, because it is the 181st day before August 28th (counting inclusively). The total presence in the period between March 2nd and August 28th, inclusive, is still 90, so the stay is legal. The same principle applies on the following day, and so on, resulting in 80 additional days of allowable presence.

In fact, an absence of 90 days from the Schengen area always allows you to return for up to 90 days.

If you have more than one visit in play, however, you will have a series of "partial resets" during your 90-day absence. For example, suppose you were in the Schengen area from the first to the fifteenth of each month between March and May. How many days can you stay when you return?

If you return

• between May 16th and July 13th, you can enter for a stay of up to 45 days
• between July 14th and July 29th, you can enter for a stay of up to 60 days
• between July 30th and August 13th, you can enter for a stay of up to 75 days
• on August 14th or later, you can enter for a stay of up to 90 days.

In short, the behavior of this rule is counterintuitive and, as you saw first-hand, it is easy to apply the rule incorrectly, even for officials who are charged with enforcing it. If you are likely to encounter that person again, it would be a good idea to put your dates into the Schengen calculator and print out the result.

If this isn't the case who is the correct authority to sort this out with?

Any and every authority with the power to enforce immigration law. Unfortunately, this probably includes the authorities you're already dealing with. Your best bet is to show them the calculator results. If this doesn't convince them, you will have to ask about an appeal, which implies some formal action against you. So you could ask them to describe the consequences if you don't leave as they say you should; this may help you identify whether the formal action would be taken by a different body (for example, immigration police instead of "local police"), and you could approach that body to see how they apply the rule.

Can you point me to official documentation for this? I need something to show to the police that this is the rule because they're telling me otherwise

Here is the (German only) text found at the (German) Federal Foreign Office, that gives a sample on how the rule should be used. I have added a rough english translation.

It takes into account that the rule must be applied in a day to day manner, so that days in the Schengen Area that may have gone out of range/scope (rolling window), are no longer taken into account.

Maybe this will be more helpfull than the original text in the Schengen Border Code Article 6(1):

For intended stays on the territory of the Member States of a duration of no more than 90 days in any 180-day period, which entails considering the 180-day period preceding each day of stay...

Berechnung der Aufenthaltsdauer mit Schengenvisum (90/180) - Auswärtiges Amt
Wie ist diese Neuregelung zu verstehen?

Nehmen wir an, ein Ausländer hat ein Jahresvisum für die Schengener Staaten, gültig vom 01.01.2019 bis 31.12.2019.
Am 18.10.2019 befindet er sich in den Schengener Staaten.

Zur Bewertung der Legalität seines Aufenthalts an diesem Tag wird der Zeitraum vom 22.04.2019 bis 18.10.2019 betrachtet.
Das ist genau der Zeitraum von 180 Kalendertagen, der am 18. Oktober endet.
Nun werden alle Tage in diesem Zeitraum gezählt, an denen sich der Ausländer in den Schengener Staaten aufgehalten hat, ein- oder ausgereist ist.

Ist die Anzahl solcher Tage nicht größer als 90, dann ist sein Aufenthalt an diesem Tag, am 18. Oktober, legal.

Wenn der Ausländer nicht ausreist, dann wird am folgenden Tag erneut die Legalität seines Aufenthalts bewertet.

Aber der Zeitraum ist dabei ein anderer, nämlich vom 23.04.2019 bis 19.10.2019 — wiederum 180 Tage; aber Anfangs- und Enddatum dieses Zeitraums sind um einen Tag verschoben.

Diese Bewertung wird für jeden Tag durchgeführt, an dem sich der Ausländer in den Schengener Staaten aufhält.

How is this new regulation to be understood?

Suppose a foreigner has a one year visa for the Schengen countries, valid from 2019-01-01 to 2019-12-31.
On 2019-10-18 they are in the Schengen states.

To assess the legality of their stay on that day, the period from 2019-04-22 to 2019-10-18 is considered.
This is exactly the period of 180 calendar days ending on October 18th.
Now all days in this period are counted on which the foreigner stayed in the Schengen countries, entered or left the country.

If the number of such days does not exceed 90, then their stay on that day, October 18, is legal.

If the foreigner does not leave the country, the legality of their stay will be reassessed the following day.

But the period is different, namely from April 23, 2019 to October 19, 2019 — again 180 days; but the start and end dates of this period are shifted by one day.

This assessment is carried out for each day that the foreigner is in the Schengen States.