If I recall correctly, it's a reference similar to the "Golden Mean" or the "Golden Ratio" which is used in visual arts compositions but is also found throughout nature. I just remember stumbling upon the rule of thirds and very much appreciating the guidance of it when struggling to pick a size for the drawer pulls. The idea is that the pulls will equal either 1/3 or 2/3 the width of the drawer to provide a pleasing visual balance. That said, there is no harm if the pulls are slightly larger or smaller. And on cabinets, there really is no rule from what I remember.
What you want to investigate is the COMFORT of the pulls. I bought several different styles and had my husband try them as his hands are much larger than mine. The pull we both found comfortable was the one I selected--I wanted one I could pull easily with one or 2 flour-covered fingers. You'd be surprised how many styles are uncomfortable to use and do NOT allow a man's fingers to actually get between the pull and the wood face.
I would mock up a few different sizes using straws or some such material and tape them on to the drawers briefly to see what length of pull appeals to you and then go from there. Good luck.
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Yes, make sure pulls are comfortable to use when getting them for cabinets.
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