I am thinking about buying the Canon Rebel T6i (750D) and currently have the T3 (1100D).
Will a lens that I have on my T3 work on the T6i ? I would like to know if I can keep my lens or if I will have to sell it with the camera.
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Yes, any lens that works on your T3/1100D will also work on a T6i/750D.
But here's something you may want to consider: When selling your old T3 you might have a hard time selling just the body. Most folks who would buy a used T3 are looking to get started in photography and probably don't already have any lenses. So you may want to include the kit lens that came with the T3 in order to make it salable.
And the current price of the T6i with 18-55mm kit lens is exactly the same as the body only at amazon and B&H right now, so why wouldn't you also get the lens if it doesn't cost extra? This happens fairly frequently when Canon has promotions on the kits.
Short answer : Yes, any lens working on a T3 will work on a T6i.
Both Bodys are APS-C cameras compatible with EF and EF-S lenses. Have a look at those posts, you will find more informations :
For you culture, you can also read :
You don't have to sell your lens. Both the T6i/750D and the T3/1100D are crop-body cameras, and can use Canon's EF-S lenses.
The Canon 7D, xxD, xxxD, and xxxxD bodies are all APS-C sensored "crop" bodies and can use EF-S lenses. You only need to worry if you're going up to a full-frame body, such as a Canon 5D, 6D, or 1DX series body.
I would also suggest that you contemplate whether a used xxD or 7D body might fit your needs better. The xxxD and xxxxD bodies are all entry-level and moving from one to another isn't as much of an upgrade in terms of hardware UI and feature improvements (e.g., dual-wheel controls, more advanced AF system, autofocus microadjust). While you will see processor/sensor upgrades, the usability of a dRebel is pretty much at a set level given its hardware limitations. And a used xxD body, one generation back, can often cost less than a current new dRebel.