US Passport Holders do not require a visa to travel to Austria for stays up to 180 days for tourism or business, however they do need a passport valid 3 months from the time of departure from Austria (6 months is HIGHLY reccomended), and at least 1 blank visa page.
Below are travel requirements for Austria per the US State Department, please cross reference this website for detailed information.
Austria is a party to the Schengen Agreement. As such, U.S. citizens may enter the Schengen area for up to 90 days in any 180-day period for tourist or business purposes without a visa. The passport used should be valid for at least three months beyond the intended date of departure from the Schengen territory, if the departure date is not known, the passport should be valid for at least six months. Please note that some neighboring countries require as much as six months of validity.
If you plan to visit Austria for purposes other than business or tourism, or if you plan to stay longer than 180 days, you can complete a research request to determine your visa requirements.
Check Swift's Schengen visa information page to see if you require a Schenghen visa. SPS does not assist with Schengen visas because you will be required to appear in person at a foreign consulate to obtain your Schengen visa. If you do not require a Schengen visa but are not a US citizen, you can complete a research request to see if you do require a visa.
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Swift Passport Services is a non-government, third party service that acts as a professional emissary between the user, the U.S. Department of State and various foreign consulates to secure Expedited U.S. Passports and Expedited Visa Service in as little as 1 business day. If you do not wish to use a third party service to obtain your passport or visa, please consult the U.S. Department of State website for further instruction.