Adding sugar to a beer recipe can raise the original gravity (OG), and can affect the final gravity (FG) depending on when and how the sugar is added.
When sugar is added at the end of the boil, it is usually fully fermentable. This raises the OG because the sugar contributes to the total sugar content before fermentation starts of course. Since the yeast consumes all the sugar, it will also contribute to lowering the FG, resulting in a drier beer.
If you're adding sugar after the initial fermentation has occurred, make sure to keep in mind the yeast's attenuation characteristics. If you know the attenuation of your yeast, you can estimate how much the FG will drop when you add sugar.
Here's how to calculate the effect of the sugar:
First determine the potential gravity contribution of the sugar: For example, table sugar has a potential gravity of 46 pound per gallon PPG. So if you add one pound of sugar to one gallon of water, it will increase the gravity by 46 points.
Second calculate the additional gravity points based on the amount of sugar added: Let's say you want to add one pound of sugar to your recipe. Multiply the PPG of sugar by the weight of sugar added. In this case, it would be 46 PPG * 1 pound = 46 additional gravity points.
Third determine the attenuation of the yeast
Fourth calculate the expected drop in FG: To estimate the drop in FG, multiply the additional gravity points from step 2 by the yeast's attenuation percentage. For example, if you added 46 gravity points of sugar and the yeast attenuates 75%, the expected drop in FG would be 46 * 0.75 = 34.5 gravity points.
Cool, I think I overcomplicated that, but hopefully this helps