Maps for Math

How do you calculate a home's heat loss?

For each wall, window, and ceiling, multiply its area by the inside-outside temperature difference and divide by its R-value. That's BTUs per hour. Add the air leaking in: 0.018 × volume × air changes per hour × temperature difference. Windows and drafts often lose more than all the walls combined.

22,240 BTU/h at 20 °F outsideΔT = 50 °F · about 6.52 kW of heatWalls1080 ft²22%Windows200 ft²22%Ceiling1500 ft²6.9%Air leaks49%biggest leak: air leaks
Heat loss at design temperature
22,200 BTU/h
Through windows
5000 BTU/h
Through air leaks
10,800 BTU/h

This leaves out floors, basements, ducts, and heat from sun and people. Sizing a furnace or heat pump takes a full load calculation (Manual J).

Challenge: Get the heat loss under 12,000 BTU/h without changing the weather.

The “design temperature”: about the coldest 1% of winter hours where you live.
Air changes per hour: how many times the house’s air is replaced by outside air each hour.
More settings
Perimeter × wall height, minus windows and doors.
Floor area × ceiling height.

Play

Swap single-pane windows for triple-pane, then seal the drafts. Which cut helps more?

Challenge: Get the heat loss under 12,000 BTU/h without changing the weather. The box under the picture turns green when you get it.

Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”

Understand

Q=∑A ΔTR+0.018 V ACH ΔTQ = \sum \frac{A\,\Delta T}{R} + 0.018\,V\,\text{ACH}\,\Delta T

Heat flows from warm to cold, and each part of the house resists it with its R-value. The flow is linear: proportional to area and temperature difference, and inversely proportional to R.

Q=A ΔTRQ = \frac{A\,\Delta T}{R}

Air leaks carry heat out directly. Every cubic foot of cold air that sneaks in has to be warmed, at about 0.018 BTU per cubic foot per °F:

Qair=0.018 V ACH ΔTQ_{\text{air}} = 0.018\,V\,\text{ACH}\,\Delta T

The bars show each part's share. The biggest one is where an upgrade pays most.

Use

Every input has a unit menu, so you can type values in the units you already have. Results follow your units.

Show the work

  1. Temperature difference\Delta T = 70 - (20) = 50\ ^\circ\mathrm{F}
  2. Walls\frac{1080 \times 50}{11} = 4909\ \text{BTU/h}
  3. Windows\frac{200 \times 50}{2} = 5000\ \text{BTU/h}
  4. Ceiling\frac{1500 \times 50}{49} = 1531\ \text{BTU/h}
  5. Air leaks: heat to warm the incoming air0.018 \times 12{,}000 \times 1 \times 50 = 10{,}800\ \text{BTU/h}
  6. TotalQ = 22{,}240\ \text{BTU/h}

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Pick the insulation and windows you have, and the coldest temperature you plan for. Open "More settings" to enter your own areas, volume, and indoor temperature.

  • Design temperatures by city are published in ASHRAE tables and many HVAC references.
  • R-values here are for the whole assembly. Framing and gaps make real walls a little worse than the insulation's label.

For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.

Cheat card

Q=A ΔTRQ = \frac{A\,\Delta T}{R}
Qair=0.018 V ACH ΔTQ_{\text{air}} = 0.018\,V\,\text{ACH}\,\Delta T
U=1RU = \frac{1}{R}
SymbolMeaningUnit
QQheat lossBTU/h
AAarea of the surfaceft²
RRR-value (resistance to heat flow)ft²·°F·h/BTU
ACH\text{ACH}air changes per hour
  • Heat loss is linear. Twice the temperature difference means twice the loss.
  • A window at R-2 loses about 6 times as much per square foot as an R-13 wall.
  • 1 kW = 3,412 BTU/h. Divide by 3,412 to compare with an electric heater.

Print this card

Where it’s used

  • Civil & Construction
    Engineers and energy auditors estimate heating loads room by room this way before sizing equipment.
  • Trades
    HVAC techs start from these same numbers, then refine them with a full Manual J calculation.
  • Home Projects
    Find where your house loses the most heat before spending money on upgrades.

Questions people ask

How do you calculate heat loss through a wall?

Area × temperature difference ÷ R-value. A 1,000 ft² wall at R-13 with 60 °F between inside and outside loses 1,000 × 60 ÷ 13 ≈ 4,600 BTU/h.

How many BTU per square foot do I need to heat a house?

It varies a lot with climate and insulation, often 20 to 50 BTU/h per square foot. That's why a heat loss calculation beats a rule of thumb.

What is an R-value?

Resistance to heat flow. Higher R means less heat escapes. Its inverse, U = 1/R, is how much heat leaks per square foot per degree. Window labels usually list U instead of R.

Sample LIN-0009 · rev 1 · model LIN-M09 · Level 3 · algebra · updated 2026-09-26