The volume of the submerged part of a floating object (in cm3) is equal to the weight of the object in grams.
Similar to Stan's answer, but with a shortcut (no need to measure the water), and possibly no water wastage.
For buoyant, rectangular objects:
I usually need to weigh something because I'm going to ship it, which means it will be packed in a rectangular box, which almost always has enough air inside for buoyancy.
I'm going to assume we're weighing such a box.
- Find or create a body of water big enough for your box to float in. I used a big cooking pot. If you don't want to waste water, use a pond, or leave the drain closed while you shower.
- Unless it's waterproof, put the box in a plastic bag. Leave the top of the bag open so the air between the box and the bag can escape.
- Lower the bag and box into the water until it is floating.
- Mark the water level on the box inside the bag (the top of the box should be level).
- Remove the box and bag from the water.
- Measure the length and width of the box, and the height up to the water line you marked, in centimeters.
- Multiply these three measurements. This gives you the volume of the submerged part of the box in cm3, which is the volume of the water displaced.
- Since 1 cm3 of water is 1 g, this number is also the weight of the water displaced in grams.
- For buoyant objects, the weight of the water displaced is equal to the weight of the object, so the volume of the submerged part of the object in cm3 is equal to the weight of the object in grams.
For irregularly-shaped objects and non-buoyant objects:
Put the object in a rectangular box that is big enough to make the object float (the technical term for such a box is "a boat"). Use the steps above to get the weight of the box by itself
A, and the weight of the box with the object
A + B. Then subtract to get the weight of the object
(A + B) - A = B.
Making your own scale out of a floating box with tic marks down the side, where you read the weight off the water level, is left as an exercise for the reader.