The formula, in one paragraph
Start with the floor area, the climate zone, the ceiling height and the insulation. Multiply them into the heat load, divide by the furnace efficiency to get the input, round up to the next standard size, and multiply the input by $45 per 1,000 BTU for the installed cost.
Step 1: Work out the heat load
The heat load is the heat your home loses on the coldest day. Multiply the floor area by the BTU per square foot for your climate zone: Zone 1 is warm at 30, Zone 2 moderate at 40, Zone 3 cold at 50, Zone 4 very cold at 60. Adjust for ceilings and insulation: ceiling height divided by 8, times the insulation factor (1.15 poor, 1.00 average, 0.90 good). At the example numbers that is 2,000 times 50, which is 100,000 BTU/h.
Step 2: Divide by the AFUE
AFUE is the share of the fuel’s heat that reaches your home, so the furnace must burn more than it delivers. Divide the load by the AFUE as a decimal: 100,000 divided by 0.80 is 125,000 BTU/h of input.
Step 3: Round up to a standard size
Furnaces come in eight standard sizes from 40,000 to 200,000 BTU. Pick the smallest size that is at least the input. At the example numbers the input is 125,000 BTU/h, so the size is 140,000 BTU — the 120,000 BTU size would fall short by 5,000 BTU/h. Always round up, never down.
Step 4: Work out the installed cost
The installed cost is $45 per 1,000 BTU of input: 125,000 times 45 divided by 1,000 is $5,625.00. A 95% AFUE furnace needs only 105,263.16 BTU/h of input, so it costs $4,736.84 installed — $888.16 less.
That box is the whole formula.
Worked example: the default home
Step 2: input = 100,000 ÷ 0.80 = 125,000 BTU/h.
Step 3: smallest standard size at or above 125,000 BTU/h = 140,000 BTU.
Step 4: installed cost = 125,000 × $45 ÷ 1,000 = $5,625.00.
Answer: 100,000 BTU/h load, 125,000 BTU/h input, 140,000 BTU furnace, $5,625.00 installed.
What changes the size most
The zone moves the size fastest. The same home needs an 80,000 BTU furnace in Zone 1 at $3,375.00, and a 160,000 BTU furnace in Zone 4 at $6,750.00. A 1,500 sq ft home in Zone 3 needs a 100,000 BTU furnace at $4,218.75. Nine-foot ceilings push the default home to a 160,000 BTU furnace at $6,328.13.
Work backwards from a furnace you already have
When the furnace is fixed, run the formula in reverse. A 100,000 BTU input furnace heats at most 1,600 sq ft in Zone 3 at 80% AFUE, and a 120,000 BTU furnace at 95% AFUE heats 2,280 sq ft. On a budget: $5,000 heats 1,777.78 sq ft and $7,500 heats 2,666.67 sq ft. Above 200,000 BTU of input, consult an HVAC pro.
Frequently asked questions
How do I size a furnace for my home?
Four steps: work out the load, divide by the AFUE, round up to a standard size, and price it. A 2,000 sq ft Zone 3 home needs a 140,000 BTU furnace at $5,625.00.
How many BTU per square foot do I need?
Zone 1: 30, Zone 2: 40, Zone 3: 50, Zone 4: 60 BTU per sq ft. Multiply by your floor area, then adjust for ceilings and insulation.
What size furnace for a 1,500 sq ft home?
A 75,000 BTU/h load, a 93,750 BTU/h input and a 100,000 BTU furnace, installed for $4,218.75.
Is a 95% AFUE furnace worth it for sizing?
Yes: it needs only 105,263.16 BTU/h of input for the same load, so it is a 120,000 BTU furnace at $4,736.84 installed.
How big a home can a 100,000 BTU furnace heat?
At most 1,600 sq ft in Zone 3 at 80% AFUE. A 120,000 BTU furnace at 95% AFUE heats 2,280 sq ft.
What if my home needs more than 200,000 BTU?
Consult an HVAC pro. A 5,000 sq ft home in Zone 4 needs 375,000 BTU/h of input, which no single residential furnace covers.
Try it: run your own numbers through the free furnace size calculator — load, input, standard size and installed cost.