The size of an envelope that requires extra postage depends on its dimensions, weight, and shape. Here are the key points from the search results:

• To be eligible for mailing at the price for letters, a piece must be rectangular and at least 3-1/2 inches high x 5 inches long x 0.007 inch thick. The maximum size is 11-1/2 inches x 6-1/8 inches x 1/4 inch thick. If an envelope exceeds any of these dimensions, it is classified and priced as a large envelope (flat) .
• Square envelopes must be at least 5 inches in size and are considered "non-machinable," subject to an additional 21-cent postal charge. A "machinable" letter is one that can pass through the USPS sorting systems with no issues.
• Large envelopes (flats) are required for shipments weighing between 3.5 and 13 ounces. They must meet specific requirements, such as being bendable and no larger than 12 inches by 15 inches.
• First-Class Mail letters that have one or more nonmachinable characteristics will pay a nonmachinable surcharge. The Postal Service charges extra postage because mailpieces that are rigid, square, or unusually shaped often jam postal equipment and are difficult to process. This costs the Postal Service time and money and may also damage your mailpiece.

Therefore, if an envelope exceeds any of the dimensions mentioned above, it will require extra postage. Additionally, if an envelope is square or rigid, it may also require extra postage. It is best to check with the post office or use the USPS Postage Calculator to determine the correct postage rate.