What size furnace does a 1600 sq ft house in Hamilton, OH need?

Notes

• Hamilton designs to 5°F, and that single number drives everything above. Heat loss is very close to a straight line in the indoor–outdoor difference, so a 65°F design difference gives 48.4 BTU per square foot per hour. The same house needs 49 MBH on a 35°F design day and 101 MBH at −20°F — a factor of 2.09, which is why a national "40 BTU per square foot" figure is useless in both directions.
• Two BTU numbers, and the box shows the bigger one. A 100,000 BTU/hr furnace at 96% AFUE puts 96,000 BTU/hr into the house; the rest goes up the flue. condensing, the common high-efficiency tier. The mistake to avoid is keeping the old input rating when moving to a higher efficiency — swapping an 80% unit for a 96% unit at the same input adds 16,000 BTU/hr of delivered heat the house never asked for.
• 100,000 BTU/hr is 24% above the calculated loss. Input ratings step in 20,000 BTU jumps and there is nothing in between, so this house lands well up the step. A two-stage or modulating furnace fixes it properly: it runs long, low and quiet at part load instead of firing full-tilt for eight minutes and stopping. Single-stage equipment at this size will short cycle through most of the winter.
• Fuel, roughly — and it does not come from the number above. 4,514 heating degree days on a 1,600 ft² house works out to about 514 therms a season, 730 dollars at the national average gas price. That figure is calibrated against what households actually burn, not scaled from the sizing rule of thumb — and the two disagree by a factor of about 2.6, because the sizing table is deliberately conservative. Going from 80% to 96% AFUE here saves roughly $146 a year against an installed price difference usually in the $1,000–2,000 range, so the payback is a real calculation and not an obvious yes.
• This is a heat loss estimate, not a Manual J. The real one counts window area and orientation, insulation R-values, measured air leakage, ceiling height, duct location and how many people live in the house. A tight new build in Hamilton can come in a third below this figure; a 1950s house with original windows and no wall insulation can come in a third above. Ask for the Manual J before signing — it costs a few hundred dollars on a $5,000–10,000 installation, and it is the only thing that turns the number above into a specification.
• Where the design temperature comes from. It is the 1st percentile of daily low temperatures at Cincinnati/Northern Ky International, 40 km from downtown Hamilton, over 2015–2024 — the same kind of airport station ASHRAE measures at. The percentile was calibrated against eight airports with published ASHRAE values and reproduces them to within 2.2°F on average. Expect a degree or two of difference from a printed table; that is far smaller than the uncertainty in the house itself.