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whats the algorithm used to resize sprite depending on the screen size /resoultion?

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I was wondering what type of forumlae is used to do this? as i want my sprites to increase in size if resolution gets bigger or maintain the ratio?

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width *= new_x_res / old_x_res;
height *= new_y_res / old_y_res;

Of course, you need to have some base resolution to go by. If your sprites aren't built specific to some resolution, or the game doesn't know what that resolution is, then it would be hard to determine the original size, much less the adjusted one.

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Make sure you use floats for your intermediate results, otherwise you'll get very strange results (assuming widht and height are ints):

width = (int)((float) width * (float)new_x_res / (float)old_x_res);
height = (int)((float) height * (float)new_y_res / (float)old_y_res);

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