What size mini split does a 500 sq ft bedroom in Youngstown, OH need?

Notes

• The "20 BTU per square foot" rule is a Midwest number. Youngstown runs 757 cooling degree days, which works out to 18.8 BTU/ft² — so for this bedroom the rule overshoots by 6%. 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.
• 12,000 BTU/hr is 28% above the load, and the gap between head sizes is wide — the next size down is 9,000. 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.
• Youngstown is dry — nights fall 22°F below the afternoon high, which only happens when there is little water in the air. Latent load is small, so nearly all of the head's capacity goes into temperature. A slightly undersized head is forgiving here: it simply runs longer.
• Do not forget the winter side. Youngstown designs to 0°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 0°F, not the nameplate, and look at hyper-heat rated equipment.
• Where these numbers come from. Youngstown-Warren Reg Airprt, 17 km from downtown Youngstown, daily records 2015–2024. Design temperatures are calibrated against published ASHRAE values at eight airports and land within about 2°F of them.