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 boiler efficiency to get the input, round up to the next standard size, and multiply the input by $55 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 boiler must burn more than it delivers. Divide the load by the AFUE as a decimal: 100,000 divided by 0.85 is 117,647.06 BTU/h of input. A 95% AFUE boiler needs only 105,263.16 BTU/h of input for the same load, which is 12,383.90 BTU/h less — and that smaller input is what makes the high-efficiency boiler cheaper to buy, before a dollar of fuel savings.
Step 3: Round up to a standard size
Boilers come in seven standard sizes from 50,000 to 200,000 BTU. Pick the smallest size that is at least the input. At the example numbers the input is 117,647.06 BTU/h, so the size is 125,000 BTU — the 100,000 BTU size would fall short by 17,647.06 BTU/h. Always round up, never down: a boiler that is too small cannot keep the home warm on the coldest day, while a boiler that is one size too big only costs a little more to buy.
Step 4: Work out the installed cost
The installed cost is $55 per 1,000 BTU of input: 117,647.06 times 55 divided by 1,000 is $6,470.59. A 95% AFUE boiler needs only 105,263.16 BTU/h of input, so it costs $5,789.47 installed — $681.12 less. The price follows the input, not the size on the box: the 125,000 BTU boiler costs $6,470.59 because its input is 117,647.06 BTU/h, not because 125,000 is printed on it.
That box is the whole formula.
Worked example: the default home
Step 2: input = 100,000 ÷ 0.85 = 117,647.06 BTU/h.
Step 3: smallest standard size at or above 117,647.06 BTU/h = 125,000 BTU.
Step 4: installed cost = 117,647.06 × $55 ÷ 1,000 = $6,470.59.
Answer: 100,000 BTU/h load, 117,647.06 BTU/h input, 125,000 BTU boiler, $6,470.59 installed.
What changes the size most
The zone moves the size fastest. The same home needs a 75,000 BTU boiler in Zone 1 at $3,882.35, and a 150,000 BTU boiler in Zone 4 at $7,764.71. A 1,500 sq ft home in Zone 3 needs a 100,000 BTU boiler at $4,852.94. Nine-foot ceilings push the default home to a 150,000 BTU boiler at $7,279.41. Poor insulation pushes it to a 150,000 BTU boiler at $7,441.18, while good insulation drops it to a 125,000 BTU boiler at $5,823.53 — a $1,617.65 difference on the boiler alone.
Boiler vs furnace: the same math, different numbers
A boiler and a furnace use the same four steps, and the same heat load: a 2,000 sq ft home in Zone 3 needs 100,000 BTU/h of heat either way. The numbers part company at the efficiency and the price. A boiler runs at 85% AFUE by default, so it needs 117,647.06 BTU/h of input, while a furnace runs at 80% AFUE and needs 125,000 BTU/h of input for the same heat. Boilers also cost more per unit of input — $55 per 1,000 BTU against $45 for a furnace — so the same home costs $6,470.59 for a boiler and $5,625.00 for a furnace. The standard sizes differ too: boilers run 50,000 to 200,000 BTU in seven sizes, and the default home lands on a 125,000 BTU boiler against a 140,000 BTU furnace.
Work backwards from a boiler you already have
When the boiler is fixed, run the formula in reverse. A 100,000 BTU input boiler heats at most 1,700 sq ft in Zone 3 at 85% AFUE, and a 150,000 BTU boiler at 95% AFUE heats 2,850 sq ft. On a budget: $5,000 heats 1,545.45 sq ft and $7,500 heats 2,318.18 sq ft. Above 200,000 BTU of input, consult an HVAC pro: a 5,000 sq ft home in Zone 4 needs 352,941.18 BTU/h of input, which no single residential boiler covers.
Frequently asked questions
How do I size a boiler 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 125,000 BTU boiler at $6,470.59.
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 boiler for a 1,500 sq ft home?
A 75,000 BTU/h load, an 88,235.29 BTU/h input and a 100,000 BTU boiler, installed for $4,852.94.
Is a 95% AFUE boiler worth it for sizing?
Yes: it needs only 105,263.16 BTU/h of input for the same load, so it is a 125,000 BTU boiler at $5,789.47 installed.
How big a home can a 100,000 BTU boiler heat?
At most 1,700 sq ft in Zone 3 at 85% AFUE. A 150,000 BTU boiler at 95% AFUE heats 2,850 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 352,941.18 BTU/h of input, which no single residential boiler covers.
Try it: run your own numbers through the free boiler size calculator — load, input, standard size and installed cost.