Is 4h30 transfer time enough to go to Madrid city center from the airport, and return?

That will be very tight schedule for 4 and a half hour layover at Madrid airport. Supposedly your flight arrives on time and you keep 2 hours (extra time) back and forth for your travel to Madrid city center, you will have 2 and a half hour remaining that means very limited hours to go and see around Madrid.

Is this enough to go to the city center and return?

Yes it will be enough just to go there and come back immediately.

Rome2Rio suggests you can take a train or subway (line 8) which takes around 30 mins to get to city center or 20 mins by taxi.

So if you are just planning to go to city center for snack or lunch, yes you can make it.

You need to allow at least 2 hours for getting from the gate to the terminal concourse and back again. Terminals 1,2,3 within walking distance (same building) and share transport connections. Terminal 4 is separate, with a different metro station. It's also big (with some gates connected by underground monorail) so it takes a bit longer to get from concourse to gate than the others, and it's further from town. The advantage of terminal 4 is it has a local railway (cercanias) connection which the others dont, but it only runs every half hour.

So you have about 2.5 hours which is rapidly eaten up by travelling to the centre. You probably have enough time to physically get to most landmarks in Madrid, but maybe not to really enjoy them.

Another issue is that single Metro tickets cost about 1.50 euros but there is now a 3 euro supplement each way on Metro tickets at the airport station, which means a return trip costs about as much as the 8.40 euro 1-day tourist pass (which doesn't require the supplement.) There are some local buses from the airport that don't require the supplement, but they offer a less direct route to town.

This true-scale map (from the official site) is displayed in all metro stations:

https://www.metromadrid.es/export/sites/metro/comun/documentos/planos/Planobasecartografica.pdf

I would suggest the following:

• Retiro park, as mentioned by Ivana

• Santiago Bernabeu Stadium, if you like soccer (Real Madrid). Just take the pink line from the airport to the end at Nuevos Ministerios, then walk to the stadium, or take the blue line one stop.

• Sol (not because I recommend it but because it's famous as km 0 in Spain) and the royal palace / cathedral which are within walking distance and have nice gardens in front. From there you can walk to Plaza de España station, which is well connected to the airport on the dark blue line 10, changing to the pink line at Nuevos Ministerios.

Near terminal 1,2,3 there is a nice park called El Capricho that it is reachable by bus and is only about 25 minutes away.

General Madrid advice: be wary of pickpockets. It's a great city, I spent 6 years there, I hope you enjoy it!

I don't suggest you to do it, seriously it's not worth it just to say you have been to Madrid, to get a minimal feeling of the city it takes some walking around. Transportation back and forth is 1.5 hr + security + finding your way around + being early at the airport. Then your mind will be on returning to the airport rather than enjoying the place. The other answers are not doing the math correctly, I think realistically you will have maybe 1 hours to do anything in Madrid.

Speaking from personal experience of doing this, yes there is more than sufficient time, providing nothing goes too seriously wrong and you are prepared to be flexible if necessary.

On my trip, I had a scheduled arrival of 10:40 and a scheduled departure of 13:55, so in fact only three hours and fifteen minutes, despite the four hours I, for some reason, say I had in my review. I managed to spend about an hour at the Naval Museum, and a good half hour or so in the airport lounge. At no point do I remember feel rushed.

If you absolutely cannot miss your onward flight, then it is probably not to be recommended.

A key point to note is that I did this on a quiet Sunday. At rush hour on Monday it would be a different story. Another point is that I found the trains a bit confusing when heading back to the airport; the destination of the train was not clear to me. So I would recommend researching the trains carefully.

The Retiro Park is a nice place to visit if you have only limited time. Take a stroll, strech your legs and enjoy some open space between flights. Maybe consult one of the fortune tellers. Visit the awesome 19th century Crystal Palace.

You can get there by subway, you will have to change trains once. I do not recall the exact travel time it takes but it is less then an hour one way.