score:2
I've edited your question to add the details from your comments. If your question is which train you will be able to catch, it's important to know exactly when you're landing (20:45, not 21:00 as originally written), which terminal you will land and if you have checked luggage or not.
German Railways gives you an estimate of 10 minutes to walk from Terminal 1 or 25 minutes to walk from Terminal 2 to the railway station. These estimates are usually excessive, so if you walk at a normal pace and are able to follow the directions without problems, you could plan with less time.
If you are scheduled to land at Terminal 1 with a domestic or intra-schengen flight (no immigration required) at 20:45 and have no checked luggage, you should have plenty of time to get to the railway station and buy a ticket before catching the 21:53 train to Karlsruhe, arriving at 23:00. From December 14th, the train departs one minute later, at 21:54. If your flight should be delayed, there are further trains departing 23:17 and 00:28.
The regular price for the train ticket, which you will have to pay if buying the ticket shortly before departure, is 40€. If you book your ticket well in advance, there are saving offers starting at 19€, but these are bound to a specific train. If your plane is delayed and you have to take a later train, the rebated ticket is forfeit and you would have to buy an additional full-price ticket for the next train. It's up to you to take this risk or not.
If the 21:53 train is not fast enough, the only realistic option to be in Karlsruhe before 23:00 is IMHO to take a taxi. The estimated price is about 220€, but with not much traffic so late in the evening, the trip shouldn't take much more than an hour and with some luck, you would be in Karlsruhe already around 22:00.
If you consider the time you need to pickup and return a rental car, it will take you longer than going by train and at least when including fuel, you are not likely to find a rental car for less than 40€.
Bus or finding a private driver (Mitfahrgelegenheit) willing to bring you are both probably the cheapest options, but if time is an issue, they are both less than ideal.
Upvote:1
Let's add another option here: car-sharing (Mitfahrgelegenheit). Here is an example site (in English). You could try a search using your arrival date and time to see if anyone is driving that route. I tried a dummy search and the route seems to be covered by both car-sharers as well as coach lines. The cost ranging between 8€ for coaches and 14€ for car-sharing.
Upvote:2
As @skv explained, the train is better than goeuro suggests, you need to use the local train company's website.
Otherwise, you can obviously get a cab or rent a car. It's probably not even quicker but it's more flexible and, given the distances involved, perfectly doable.
Upvote:3
For future travels: there is a special offer to book your train ticket with the flight, called Rail&Fly (or AirRail for a few selected destinations).
Rail&Fly is an offer of the airlines and tour operators and can therefore only be booked by them.
These tickets are not bound to a specific train.
- from/to each of the over 5.600 DB train stations
- from/to any German airport as well as Basel and Salzburg Airport on the entire DB rail network. Below, please find a list of all connecting services to and from airports which are included free of charge in your Rail&Fly ticket.
- flexible in all DB trains (including ICE) except for Motorail und charter trains. City Night Line and Sprinter trains with extra charge.
- valid on the day before your flight departure, the day of the flight departure, the day of your return and the following day.
Upvote:5
Ok there are two things, while searching trains in Germany Bahn.de has been my best site. I have even used them to book hotels in Paris, its very informative and useful.
Second confusion may have been caused due to the Frankfurt airport station.
Frankfurt(Main) Flughafen is the name you are looking for if you look at the main (Frankfurt (Main) Hauptbahnhof) station the information would be different.