How many people live in the city of Madrid?

How to get close to this number

Take the national population and apply a capital share. The country has just under fifty million people, and a dominant capital typically holds somewhere around seven percent of a European nation in its city limits. That fraction gives a figure in the low millions, and the explanation adds the metropolitan figure at roughly double.

The city-versus-metro distinction is the recurring trap in every urban question on this site, and it is worth internalising once: administrative city figures and metropolitan figures routinely differ by a factor of two or more, and which one is quoted changes the answer more than any uncertainty in the data.

The altitude detail is the one that explains the climate: at six hundred and fifty metres this is the highest capital in Europe, which is why summers are dry and winters are genuinely cold rather than merely mild. A population question turns out to also carry the explanation for why the city does not have the Mediterranean climate its latitude suggests.