I'm passing through Canada, on my way to somewhere else. I'm staying only a short time.
Is there a website, or some other way of find out out if I need a visa?
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Here is a Canadian government website that will lead you through the steps of discovering whether you need a visa to visit Canada, whether briefly in transit or for a more extended visit.
You can enter your country of citizenship and all other information about your trip, and it will tell you if you need a visa, and what visa you need.
Some general rules:
You can apply for a transit visa by filling out the application for a Temporary Resident Visa and selecting transit visa from the list of options on the form. You may not need a transit visa if you are travelling to or from the United States.
If you are in doubt about your eligibility you can contact your nearest Canadian embassy by email or otherwise.
Whenever I had similar doubts, I always wrote a short email to the embassy of the country in question (Canada in your case) in my country. The embassy officers have been very helpful in most cases and answered promptly. Additionally I printed these emails and took them with me on my trip. While I don't think a piece of paper will be of any help in a difficult situation, it made me sleep well :)
The Transit Without Visa (TWOV) program allows eligible foreign nationals to transit through Canada without a visa or an eTA. At present, the TWOV program operates at the Vancouver International Airport in British Columbia, Canada, the Calgary International Airport in Alberta, Canada, the Winnipeg International Airport in Manitoba, Canada and Toronto's Pearson International Airport (Terminal 1 only) in Ontario, Canada.