Measure the finger, not an old ring
Measure the finger with a ring gauge or a strip of paper at the intended position, at room temperature, because fingers change size through the day. A ring measured from an old ring reflects that ring's wear, not the current fit.
Record the measurement as an inner diameter in millimetres, then convert once to the size system your market uses.
Converting US, EU and UK sizes
US, EU and UK sizes are different scales, and rounding between them introduces error. Keep the millimetre diameter as the master value in the order and let the supplier convert from it.
For wide bands, add allowance: a 6 mm band feels tighter than a 2 mm band at the same inner diameter.
Sizing in bulk orders
Bulk orders are bought as a size curve. Confirm the curve, the tolerance per size and whether half sizes are available before production; changing the curve after casting means new molds or rework.
State the sizing system on the purchase order and on the packaging label so retail staff and customers read the same number.