This question was asked about measuring recipes. If you live where you must use metrics I can only offer you a little help. My dear friend in BC could answer our questions as how to make the change. I offer this web site for a really nice group of charts.
As for the tea cup and mug...
If your tea cup is like mine it will measure on the inside;
5 1/2 mm deep to 7 1/2 mm across it will hold less water than a cup and a little more water than 3/4 cup.
The mug if it is like mine will measure 8 1/2 mm deep to 7 1/2 mm across and it holds 1 1/3 cups of water.
A spoon you eat with holds 1 teas of water. A bigger spoon like what I stir with holds
1 tablespoon of water just barely.
My hands are not med and not small just between those and I can hold 1/3 cup of dry goods in one hand if you want to measure that way.
If you have a way to measure these in other than metric just know that on my ruler 1 inch is about 2.5 mm. The inch is just a little touch bigger.
WOW that's my math for the day...Any ideas out there?