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Chiang Mai is a beautiful and cultural city in the North of Thailand, the distance between there and Koh Phangan is 1450 km.
There is no direct way to get to Koh Phangan as the island does not have an airport however you can get as close as Koh Samui next door or to Surat Thani on the mainland. There are more options however, other than traveling by air.
This is the most expensive yet convenient way to travel to Koh Phangan. You can fly direct to Koh Samui (most expensive) which is then just a 30 minute ferry ride to Phangan. Otherwise you can fly to Bangkok then connect to Surat Thani and take the Raja Ferry (2.5 hours) to the island.
Minibus/taxi and ferry ticket from Koh Samui Airport to Koh Phangan should be no more than 1000 Baht and the same from Surat Thani. Both can be easily booked from the information and travel desks when you reach the airport or you can book online.
The closest ferry company pier from Koh Samui airport is Seatran, this ferry brings you to the main port of Koh Phangan, Thong Sala. All other ferry companies also bring you into Thong Sala apart from the Haad Rin Queen boat which takes you to Haad Rin. All locations on the island are easily accessible from Thong Sala and for
Haad Rin just 15 minutes more.
The cheapest way to travel to Koh Phangan from Chiang Mai is by bus and ferry or train, bus and ferry. Train from Chiang Mai to Bangkok takes about 13 hours with and then another 12 hours to get from Bangkok to Surat Thani and so takes a long time.
Tickets range from 400 to 1,800 Baht depending which class carriage.
From Surat Thani railway station which is located in the nearby town of Phun Phin you can get a joint ticket to Koh Phangan from Raja Ferry or Seatran Discovery which range from 400 - 700 Baht. Or, go to Donsak Pier and hop on a boat to Koh Phangan from there.
If you want to avoid the train and travel only by bus from Chiang Mai to Koh Phanga you will need to get to Bangkok by bus and change buses there.
Travel time and ticket prices are roughly 11 hours and from 500 Baht from Chiang Mai to Bangkok.
Then a 9 hour journey from Bangkok to Suratthani costing roughly 400 Baht or you can pay more for VIP bus which is about 800 Baht.
From Surat Thani bus station you can then get a combination bus and ferry ticket to Koh Phangan.
Enjoy your trip down!