I have already answered a question like this, but now that I have more knowledge on this subject, I will answer this question again with a more factual approach.
Original answer: Titus Waddimba's answer to What might have happened if the US had won the War of 1812? (thanks for 50k views and 800+ upvotes btw).
Note: This had little chance of happening.
In order to make this scenario work, I am just going to naively assume that the following factors result in a British defeat for whatever reason.
- Issac Brock, the man most responsible for preparing Upper Canada for a war with the USA catches a disease and dies.
- In April 1813, the USA sticks to the original plan and attacks Kingston, which was a much more strategically vital target.
- In May 1813, after the capture of Fort George, the Americans pursue the retreating British, preventing the British counterattack at the Battle of Stoney Creek, resulting in Upper Canada being essentially defenseless.
- Britain is more war-weary after the Napoleonic Wars, and sees Canada as a lost cause, and agrees to a peace treaty on unfavorable terms.
So, after all of the following circumstances, Britain agrees to peace. This alternate Treaty of Ghent results in Rupert’s Land, Upper Canada (Ontario), and Lower Canada (Quebec) being ceded to the United States. Britain would retain the Maritime Provinces and Newfoundland, due to their superior navy.
Canada wouldn’t like the idea of being absorbed into the U.S. at all. Most of Canada’s population were loyalists who had fled from the 13 Colonies during the American Revolution. For the first few years following the War of 1812, there would be an insurgency in the Canadas (Quebec especially). Gradually, the insurgency would die down (but for Quebec, it would take much longer).
North America: 1830
By 1837, Ontario would have assimilated into the U.S. (mostly due to the mass migration of New Englanders into the Canadas), but Quebec would prove to be the biggest can of worms. Quebec is majority French-Speaking and is far less culturally homogenous with the USA than Ontario is. This would result in Quebec still rebelling in 1837. Britain would intervene to aid the Quebec rebels and reconquer Canada.
As shown in the Crimean War, Britain was terrible at amphibious landings, due to that and the Americans having more troops (on their home soil), the Americans would win this “War of 1837”, and that would result in the Maritimes being absorbed into the United States as well. It is possible that the British still retain Newfoundland at least because again, superior naval power.
During the early 19th Century, there was a very delicate balance between Free and Slave states in America (free states having Slavery illegal, while slave states having slavery legal). The land from Canada would cause a huge imbalance of power in favor of the free states, so the Missouri Compromise line would be negotiated further north, and the South would need more land for slave states. This would result in Texas being annexed much earlier (likely immediately after the War of 1837), and the Mexican-American War. The United States would still win, but in this world, they would take a far larger chunk of Northern Mexico and annex the Yucatan.
North America: 1845
If the Slave and Free states aren’t balanced by this point, then the U.S. would have more imperialistic adventures in the Caribbean than in our world. The South wanted to expand Southward for more space for plantations and tried to conquer parts of Central America. The North didn’t approve of this at all, but in this world, the North would let *some* of their ambitions slide to finally restore balance.
North America: 1859
North America: 1861 (American Civil War)
Just like its northern counterpart, the Confederacy would be larger in this timeline, stretching from the Atlantic Ocean to the Gulf of California. Due to the Americans owning territory on both sides of Mexico, a war with France is more likely in this timeline (since they were trying to invade and colonize Mexico).
The Civil War would have the same result (but would last a few months longer). The North would win, the CSA would be dissolved, etc. After the war, the USA would still purchase Alaska from Russia (since Russia was broke after the Crimean War), and may even purchase Greenland and Iceland, too. William Seward, the same Secretary of State who purchased Alaska, wanted to purchase Greenland and Iceland as well. With ownership of Canada, this would be more geographically feasible.
A more imperialistic the United States may have ended up annexing Cuba in 1898 or 1902.
North America: 1914
The rest of history is almost exactly the same (although Britain would be more disadvantaged in both world wars). Quebec would essentially be another Louisiana, eventually become majority English speaking as newer generations of Americans would move in from New England, becoming the majority. The USA would never get involved in Panama and would build the canal in Nicaragua instead.
The USA would have a significantly higher Spanish and Latino population, so there would be debates on if Spanish should be an official language (due to more land being taken from Mexico, annexation of Cuba, etc).
Feel free to correct me if I got anything wrong. Have a nice day.