Transortation in Copenhagen

There is a large ticket office and ticket machines just before the metro station at the airport, you can hardly miss it. The 24 hour ticket is valid for all public transport including trains, metro, bus and harbour buses (boats).
Have you done the math to see if the 24 hour ticket is worth it?

http://www.visitcopenhagen.com/copenhagen/transportation/tickets-prices

Where to buy tickets in person

Always buy a ticket before boarding the train or metro. You can buy
your ticket in ticket machines, which accept Danish cash and the most
common credit cards, or 7 Eleven kiosks at the train and metro
stations. In Copenhagen Airport arrival hall and at Copenhagen Central
Station there is a DSB ticket office as well as ticket machines.

City Pass

The City Pass gives you unlimited access to buses, trains, metro and
harbour buses in zones 1 - 4, which includes the centre of Copenhagen
and to and from the airport. An adult 24-hour City Pass costs DKK 80
and an adult 72-hour City Pass costs DKK 200.

Airport to central train station cost 36 dkk one way. Single trip two zone coast 24 dkk and I think the single trip allows for one hour. Copenhagen is very walkable (realtively compact, flat and scenic). Bus drivers give change.

Thank you!
How does a 24 hr count? If I will start using at 2 PM of Monday, can I still use it until 2 PM of Tuesday or it ends at midnight of Monday? Thanks.

How does a 24 hr count?

We were told that the 24 hour clock starts when purchased.

Be sure to get the right ticket for your needs. The one called 24 hour ticket is valid for all zones in greater Copenhagen and costs 130kr, which also includes Helsingør, Roskilde and Hillerød.
The city pass is valid for zones 1-4 (Airport and city centre) and costs 80kr.
Use www.rejseplanen.dk to look at schedules, routes and prices for all public transport in Denmark.

Thank you for all your answers.
We will be arriving at 1:55 PM on Monday and start our cruise on Tuesday. We want to maximize our limited time in Copenhagen . I realized that these are 2 different things. Will city pass be our better option over the 24 hr pass? What places can you recommend we visit late afternoon on Monday that are open? early morning of Tuesday? We can walk so we plan to follow Rick Steve's city walk. Thanks again.

We bought out City Pass at the train station.