On Købmagergade is the Round Tower (Rundetårn), a 36-meter-high structure built as an observatory in 1642.

 It now also houses a small collection connected with the famous Danish astronomer Tycho Brahe. A particular treat is the platform, reached by a wide spiral ramp. From the top are magnificent panoramic views over the city. A new attraction is the glass floor hovering 25 meters above the ground where you can peer down into the castle's core. 

Fans of Hans Christian Andersen will be interested to know that the tower features in his well-known story The Tinderbox - "eyes as big as the Round Tower.