Karlstad is a smaller airport in Sweden. You can fly to 0 destinations with 0 airline in scheduled passenger traffic.
FlightsFrom.com is a useful website for finding airline routes and flight schedules globally. The idea is being able to explore destination opportunities through non-stop flights from a specific airport. It's a tool to set up your business meeting or weekend holiday based on your timeschedule and your closest airport.
Many mainstream sites don’t list low-cost carriers or link transoceanic flights to regionally based carriers that can provide less expensive options. For that, you need a bigger tool kit… (Hint: search by destination airport at FlightsFrom.com)
Many low-cost carriers airlines prevent their flights from showing up on some of these (read Vayama or Google Flights) third-party travel websites. If you want a chance to view all local departures, try using FlightsFrom.com