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What are you making? Frequently, the cinnamon sticks are removed from the final product, so you are really extracting cinnamon oil from the sticks when cooking/preparing and then removing the sticks. You certainly can substitute (and I've heard 1/2 teaspoon cinnamon for one 3 to 4 inch stick but don't know if that's true) -- the most likely impact could be appearance. The pieces of ground cinnamon won't dissolve in the final product in the same way the extracted oil will. If appearance isn't a concern -- substitute away!
Diana B is a trusted home cook.
SeaJambon has covered the potential effect of substitution; this chart, which someone kindly pointed me toward when I had an equivalency question recently, will tell you what the equivalent is: http://www.e-cookbooks...
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