What size water heater does a household of 6 in Pocatello, ID need?

Notes

• Buy first hour rating, not gallons. FHR is what the heater actually delivers in the busiest hour — the water already hot plus whatever it reheats while you use it. Two 50-gallon heaters can differ by 30% in FHR because the burners differ. This household needs about 137 gal, which a 100 gallon gas tank covers.
• Pocatello water comes in at about 48°F, and that is the number that decides tankless. Reaching 105°F at the tap is a 57°F rise here. Delivering 4 GPM across it takes roughly 114,000 BTU/hr. The identical shower needs 56,000 BTU/hr in south Florida and 130,000 in the upper Midwest — 2.32×. The box did not change; the water did. This is the single most common way a tankless unit disappoints: it was sized off a national chart.
• The peak hour decides the size, not the daily total. Nobody runs out of hot water at 2 pm. What matters is 6 showers plus the kitchen inside one morning, and a heater sized on daily average fails that hour every day.
• Pocatello is cold-water territory, and it changes which technology makes sense. A whole-house tankless here needs 114,000 BTU/hr, which usually means a 199,000 BTU unit and often a gas line upgrade — the 57°F rise is what drives that, not the number of bathrooms. A tank, or a tank plus a small tankless at the far bathroom, is frequently the cheaper answer in this climate.
• Electric tanks recover far slower than gas. A gas tank refills its 100 gallons in well under an hour; a standard electric one takes roughly twice as long — and in Pocatello, with a 57°F rise, that gap widens. If the house is electric, go a size up or look at a heat-pump water heater.
• Where the incoming temperature comes from, and when it is wrong. It is the annual mean air temperature at Pocatello Regional Airport, 14 km away — shallow groundwater equilibrates with the climate above it, so the two track closely. A city that draws from a shallow lake or river does not follow this rule: Chicago's Lake Michigan supply runs colder in late winter and warmer in late summer than the figure above. If your utility publishes a monthly source temperature, use theirs.