The airline says ‘the delay was less than three hours’: is that right?

How delay is calculated in general is covered in how flight delay is calculated. Here the focus is the reply you have received.

Arrival decides, not departure. You may be entitled to compensation when you reach your final destination three hours or more after the scheduled arrival time (C-402/07, para. 61). A late departure that is made up in the air does not count.

Arrival is the door, not the touchdown. The Regulation does not define the term, but the Court of Justice has held that arrival time is the moment at which at least one of the doors opens, provided that passengers are allowed to leave the aircraft (C-452/13, para. 25). The Court noted that the passengers' situation does not change significantly when the wheels touch the runway or when the aircraft reaches its parking position, because they are still subject to restrictions on board (paras 23 and 24).

The airline's own timing is not decisive. In the Germanwings case it was precisely the airline that argued the touchdown time should apply (para. 9). The Court also rejected the idea that the parties can fix the moment themselves (para. 18).

The final destination counts. If you had several flights on the same booking, it is the delay at the final destination that matters, meaning where your last flight goes (C-11/11, para. 35, and Article 2(h)). An airline that measures the delay on the first leg can therefore arrive at a different figure from the one that applies to the whole journey.

The same booking is the key. Flights on a single booking form a whole (C-537/17, paras 18 and 19). How this works when tickets were bought separately is covered in separate tickets and a missed connection.

A 50% reduction is a separate question. For some long flights compensation may be reduced by half if the arrival is less than four hours late (C-402/07, para. 63). That affects the amount, not whether a right exists.

Which moment does the figure refer to? A reply that merely states ‘2 hours 50 minutes’ without saying whether it means touchdown, parking position or door opening cannot be tested. That is the first thing to clarify.

Evidence from more than one place. Your own papers, such as boarding passes, the booking confirmation and messages from the airline, can be supplemented with independent flight data on actual times.

Extraordinary circumstances are a separate question. Even if the delay is three hours or more, the airline may show that it was caused by such circumstances (Art. 5(3), C-402/07, para. 69). That is assessed separately, see when the airline cites extraordinary circumstances.