How long does it take to walk the Royal Route in Prague? And how much time should we estimate for Prague Castle? Thanks!

It depends on how much time you usually spend on looking at things, I'd say, I don't know how to define it for you (in terms of the castle). You could spend all day there if you wanted, there are various things to see in the area on the castle grounds and around it (like the National Art Gallery). So who knows. If you mean the castle itself only, maybe an hour as a guess.

Same for the Royal Route, if you literally mean just walking it, and at a good pace, just figure out the distance and how fast you walk. I think it's about 2.5 km, maybe 3. So you could easily walk that in less than an hour. But if you decide to stop at lots of places along the way, it could certainly take a whole day, I'm sure. I'd schedule at least a half day for it, maybe more if you like looking in shops a lot.

I would agree with Christina.
If you do the Royal route back to front ie go to the castle area first spend whatever time you want there and then follow the route in reverse you can finish up at the Powder tower and the magnificent Municiple house where there are several bars/resturants within to just put an amazing finish to your day.
The Namesti Republiky metro is a very short walk away from there so you can easily get back to any part of the city faily quickly.

If you are going to do the Castle, the various other buildings in the complex, including the cathedral and then walk down the Golden Road I would allow 4 hours unless you like to whip though everything and not look at anything in detail.

Thank you...I only have 2.5 days in the city, and I am trying to plan an itinerary, so I just wanted some kind of idea of how long to allocate for the castle/royal route.

With 2.5 days in Prague, I'd spend a day on each side of the river. Use, modify, or ignore as you wish.

-for one day: Prague Castle and its churches and museums for at least half a day, plus visits to a couple churches on that side of the the Moldau (Loreto Church, Church of St. Nicholas, Church of Our Lady Victorious) and Wallenstein Palace and Garden as time permits.

-for another day: Old Town Hall and Clock (be there on the hour to see it strike and run), Tyn Church, Powder Tower, Jewish section including allied cemetery and synagogues and museums, Bethlehem Chapel, National Museum. While walking along, keep an eye out for the architecture in general (stunning) and walk through Wenceslas Square. On at least one of these days, walk across Charles Bridge.

-for half a day: Vysehrad.