Close to nothing, but not zero
USDA’s survey figure for hot chocolate made with milk is 3 mg of caffeine per 100 g, which comes to about 7 mg in an 8 fl oz cup. That’s a fraction of an 8 oz cup of drip coffee at USDA’s reference strength (95 mg), and even less than a cup of decaf coffee, which the FDA puts at 2 to 15 mg. The cocoa in hot chocolate is real cocoa, and cocoa solids carry caffeine, but a mug is mostly milk and sugar with only a spoonful of cocoa doing the work.
A coffee-shop version runs a bit higher because it’s made stronger. A Grande Starbucks Hot Chocolate carries 25 mg, and Starbucks notes that this matches a Grande decaf Pike Place Roast, worth knowing before handing one to a child on the assumption it’s caffeine-free.
Why cocoa strength varies so much
The caffeine comes entirely from how much actual cocoa solids end up in the cup, and that varies a lot by recipe. USDA’s figure for unsweetened cocoa powder alone is far higher, 230 mg per 100 g, but a mug of hot chocolate uses only a small fraction of that in cocoa before it’s diluted with milk. A cup made rich and dark, or doctored with extra cocoa powder, will carry more than USDA’s 7 mg reference figure; a packet mix built more from milk chocolate than cocoa powder tends to carry less, since milk chocolate itself is comparatively low in caffeine.
Where it matters
For most adults, 7 mg in a mug is not worth tracking; fifty-plus cups would be needed to reach the 400 mg daily figure the FDA cites for healthy adults. It matters more for the people caffeine limits are strictest for: children, and anyone in pregnancy following the 200 mg daily ceiling ACOG uses, where a coffee-shop hot chocolate (25 mg) is a more meaningful bite of the day’s allowance than a home-made cup. Read the cup, not just the name: “hot chocolate” on a chain menu can be several times the home-made figure.