What size mini split does a 400 sq ft bedroom in Dubuque, IA need?

Notes

• The "20 BTU per square foot" rule is a Midwest number. Dubuque runs 728 cooling degree days, which works out to 18.6 BTU/ft² — so for this bedroom the rule overshoots by 7%. A single national figure has to be wrong somewhere, and this is where.
• Bedroom: the room where oversizing hurts most — quiet, low load, long runtimes wanted.
• 9,000 BTU/hr is 21% above the load, and the gap between head sizes is wide — the next size down is 6,000. In a single room that matters more than it would on a central system: there are no other rooms to absorb the excess capacity. If the room is well insulated and shaded, the smaller head is usually the better buy, and modern inverter compressors modulate down far better than they modulate up.
• Dubuque is fairly dry — summer nights stay within 20°F of the day's high, the signature of humid air. A meaningful share of this head's work is removing moisture, and it only removes moisture while it is running. This is the climate where an oversized head produces a room that reads cold and feels clammy.
• Do not forget the winter side. Dubuque designs to -10°F. That is cold enough that a standard head will have lost a large part of its rated capacity by the time it is needed most — check the manufacturer's capacity table at -10°F, not the nameplate, and look at hyper-heat rated equipment.
• Where these numbers come from. Dubuque Regional Airport, 53 km from downtown Dubuque, daily records 2015–2024. Design temperatures are calibrated against published ASHRAE values at eight airports and land within about 2°F of them.