There is no official skipping stone. There is a range that keeps working: a disc wide enough to plane, thin enough to bite, heavy enough to keep its line, light enough to snap. These are starting numbers, not commandments. The water still has a vote. Optimal size, shape, and weight means: a stone you can actually throw, not a specimen in a case.
Diameter
Most throws like a stone between about five and eight centimetres across — a biscuit, not a dinner plate. Smaller stones skip if the water is kind; they are harder to spin well. Larger stones skip if you have the arm; they punish a sloppy angle and a late release.
Measure against your palm, not a ruler, once you have a feel. The first time, a ruler is honest. After that, your hand is faster.
Thickness
Aim for something you can describe as a disc: often eight to fifteen millimetres. Thicker than your thumb and you are throwing a brick with manners. Paper-thin and the stone may shatter on the first hit, or flex and die. Parallel faces matter more than a perfect millimetre.
A wedge that is thin on one side and fat on the other is a keel in disguise. Reject it even if the average thickness looks right.
Weight
A useful pocket range is roughly forty to one hundred twenty grams. Around eighty to one hundred grams is a common sweet spot for an adult sidearm: heavy enough to hold a line across small chop, light enough to flick. You will not weigh stones on the beach. Weigh them in the hand: a decision, not a burden.
Children sit toward the low end of that band. A stone that feels like a decision in a small hand is already too much stone.
Shape
Round or oval discs are the easiest to learn on. A slight triangle can work if the faces are flat — some throwers like a bit of a point to index the grip. Avoid pronounced keels, deep cups, and anything that wants to be a boat. If it rocks when you set it on a table, it will rock on the water.
Symmetry helps spin. A lopsided disc can still skip; it will argue about line. Learn on the boring ones.
A starting set
If you are learning, gather five stones in that diameter and weight band, all flatter than they are thick. Throw the same stretch of water with all five before you blame your arm. The stone is half the skip; the other half is how you throw it.
For why these shapes plane at all, read The Science of Skipping Rocks. For how to find them without stripping a beach, read How to Choose a Skipping Rock.
What size skipping stone should I use?
Start near a biscuit: five to eight centimetres, a disc you can pinch, a mass that snaps rather than thuds. Adjust after a handful of throws. If every stone dives, the size is probably not the first problem — the angle is. If every stone dies after a slap, look at thickness and keel.