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A kitchen scale and tap water give you true capacity in millilitres in about two minutes.
Printed capacity is usually measured to the rim. The volume you actually use — to the drinking line, with headspace — is smaller, and the only way to know it is to measure.
The tool is a kitchen scale, because water makes the math free: 1 g of water is 1 ml. Put the empty mug on the scale, tare to zero, and fill to the level where you would actually drink.
Read the display as millilitres. If you think in ounces, divide by 29.57 — 325 g of water is 11.0 fl oz, and 444 g is 15.0 fl oz. The whole procedure takes about two minutes.
On narrow screens, swipe or scroll the plate sideways.
A ruler cross-check catches scale mistakes. In a mug with an 85 mm inner diameter, 300 ml of water stands about 53 mm deep; if your measurement and your ruler disagree by more than a few millimetres, re-tare and repeat.
Use the number twice. First, compare it with your usual serving — a 12 fl oz pour wants about 444 ml for an 80 percent fill — and second, match it to a vessel class on the size chart before you shop for a replacement.
Repeat the test whenever a label looks optimistic, and note the material while you are at it: the wall type from the materials comparison changes how long your measured volume stays inside the 60 to 65 °C drinking window.
Further reading