You could place the multi-component object on a narrow, raised edge, move it around until you find a balance point. Mark the axis of balance. Repeat the process along other axis. Why do you need to know?

 

Best way to do it without a computer is to weigh and measure each individual part before it gets glued up.

So for a table you would have a minimum of: table top, 4 aprons, 4 legs. The center of gravity of each piece is the center of volume essentially. The way to find out overall center of gravity is to take each pieces weight and multiply it by the distance of the pieces center to the floor (for vertical center). Add up all of these numbers and divide by the total weight.

Say your top is 5lbs, each apron is 2 lbs, each leg is 1lb. Table is 30" tall with a 2" thick top and 4" aprons. So the top vertical sum would be 5lbx29" (30" minus half the thickness) = 145. Aprons is 2lbx26" (30" minus 2" top, minus half apron thickness of 4") = 52×4 aprons = 208. Legs are 1lbx14" (30" minus 2" top, divide in half for leg) = 14×4 legs = 56. Overall vertical moment is 145+208+56=409. Total weight of 5lb+4×2lb+4×1lb = 17lb. 409/17lb = 24.05" vertical center of gravity.

 

I'm trying to make something that balances an object resting in it. There are plans available but I'd like to make it for a custom sized item. I would like to avoid as much cutting and recutting as possible.

 

The center of gravity is at the end of the heaviest drawer.

 

I think we could make better suggestions if we had some idea of what you are trying to make. Can you provide some sketches, or photos?

 

Well for one project it was one of the single board self balancing wine bottle holder. I don't want to use a bottle of wine I'd like to customize it with a decorative board and either a whiskey bottle or rum bottle. But not a standard shaped bottle.

 

It will be very difficult to design a balancing bottle holder that would work for varying bottle shapes & sizes.

 

O, that's not so bad. Learning CAD is highly involved, and you'd have the added complexity of modeling partially filled bottles. I would just take your bottle and balance it on your finger to get the center point(s). Then make the balance board bottom land directly under them.

I would make the hole fit so that the bottle is horizontal, that way the partial center of gravity will stay near the same place as it gets drunk (drinked)

 

I've made these before. If the bottle has a long-ish neck then fortunately you have some leeway finding the balance point. The other thing you can do is make the thing, test it, and just re-cut the angle on the bottom, or the overall length until it works.