Heat Transfer Calculator

How this calculator works

Heat moves in exactly three ways, and a building uses all of them at once. Conduction carries heat through solid material — through drywall, insulation, sheathing and siding in series, each layer adding resistance. Convection carries it between a surface and the air or water moving past, which is why a windy day feels colder than a still one at the same temperature. Radiation carries it between surfaces that can see one another, through vacuum if necessary, at a rate governed by the fourth power of absolute temperature. This calculator handles each mode in its own tab, in the form the HVAC trade actually uses.

The wall and roof tab builds an assembly layer by layer. Every layer contributes a resistance — an R-value in inch-pound units, an RSI in metric — and those resistances add in series along with the air films that cling to each face. The reciprocal of the total is the U-factor, and heat flow follows as U times area times temperature difference. The layer table shows how much of the total resistance each component supplies and what the temperature is at every interface, which is how you find out whether the sheathing sits below freezing or the drywall below the dew point.

Thermal bridging is handled by the parallel-path method. Studs conduct roughly ten times more readily than the insulation between them, so the calculation is run twice — once through the cavity, once through the framing member — and the two are blended by their share of the wall area. This is the difference between the R-value printed on the batt and the R-value the wall actually delivers.

The remaining tabs cover pipe insulation, where conduction is radial and each added inch buys less than the last; convection by Newton's law of cooling, alongside a radiation estimate so the two can be compared honestly; and radiation by the Stefan-Boltzmann law, with a table showing how sharply the fourth-power relationship bites.

The formula

Conduction through layers, in series:
    R_total = Σ (thickness ÷ k) + R_inside film + R_outside film
    U = 1 ÷ R_total
    Q = U × A × ΔT

Thermal bridging, parallel path:
    U_average = f × U_framing + (1 − f) × U_cavity

Radial conduction through pipe insulation:
    Q/L = 2π k (T₁ − T₂) ÷ ln(r₂ ÷ r₁)

Convection, Newton's law of cooling:
    Q = h × A × (T_surface − T_fluid)

Radiation, Stefan-Boltzmann:
    Q = ε σ F A (T_surface⁴ − T_surroundings⁴)
    σ = 5.670374419 × 10⁻⁸ W/m²·K⁴          absolute temperatures
    h_r = ε σ (T_s² + T_sur²)(T_s + T_sur)   linearised equivalent

The conduction relation is Fourier's law integrated across a slab, and the reason resistances add in series is that the same heat must pass through every layer in turn. For a cylinder the area grows with radius, which is where the logarithm in the pipe equation comes from — and why doubling insulation thickness never halves the loss. Newton's law of cooling is a definition as much as a law: it defines the coefficient h, which must then be measured or correlated for each geometry and flow condition. The Stefan-Boltzmann constant follows from the SI defining constants and is quoted here at the CODATA 2018 value.

Air film resistances, material R-values and surface coefficients are the published design values of the ASHRAE Handbook — Fundamentals, chapters 25 through 27: R-0.68 h·ft²·°F/Btu for an indoor wall surface, R-0.17 for an outdoor surface in the 15 mph winter design wind, R-0.45 for half-inch gypsum board, R-3.14 per inch for fibreglass batt, and so on. Thermal conductivities and emissivities follow Incropera and DeWitt, Fundamentals of Heat and Mass Transfer. The parallel-path framing method is the one described in ASHRAE Fundamentals chapter 27. Dew point uses the Magnus formula with the coefficients of Alduchov and Eskridge (1996), which is accurate to about 0.4 °C over normal building conditions.

Manufacturers publish tested values for their own products, and those govern over any table. Insulation conductivity in particular rises with mean temperature, so a k value taken at room temperature understates the loss from a hot line.

Worked example

A 100 ft² wood-framed wall on a 10 °F design day, the calculator's default: half-inch gypsum board, an R-13 fibreglass batt in a 3½-inch cavity, 7/16-inch OSB sheathing and hollow-backed vinyl siding, with the room at 70 °F and 40 percent relative humidity.

1. Layer resistances: gypsum 0.45 + batt 13 + OSB 0.62 + siding 0.61 = R-14.7
2. Air films: indoor wall 0.68 + outdoor winter 0.17 = R-0.85, giving R-15.5 total (RSI 2.73)
3. U-factor: 1 ÷ 15.5 = 0.0644 Btu/h·ft²·°F
4. Heat flow: 0.0644 × 100 ft² × 60 °F = 386 Btu/h (113 W), a flux of 3.86 Btu/h·ft²
5. Inside surface: 70 − 3.86 × 0.68 = 67.4 °F, comfortably above the 44.6 °F dew point — no condensation
6. Across the batt alone the temperature falls 50.2 °F, from 65.6 °F to 15.4 °F, which is 84 percent of the total drop

Now switch framing on at 23 percent, the usual figure for 2×4 studs at 16 inches on centre. Along the framing path the batt is replaced by solid wood at R-4.4, so that path totals R-6.9 rather than R-15.5. Blending the two by area gives an effective R-12.1 and raises the heat flow to 497 Btu/h — 29 percent more than the cavity figure alone. That gap is why continuous exterior insulation, which covers the studs as well, has become standard practice.

Assumptions & tips

• Never omit the air films. Together they contribute about R-0.85 to a wall — more than half an inch of plywood — and they are the reason the inside surface of even a poor wall stays near room temperature. They are also the only resistance a bare single-pane window has beyond the glass itself.
• Insulation obeys diminishing returns. Going from R-5 to R-10 cuts heat flow in half; going from R-30 to R-35 cuts it by 14 percent. The first inches always matter most, which is why insulating an uninsulated wall pays back faster than deepening an already-thick attic.
• Watch the surface temperature, not just the R-value. Condensation is a surface-temperature problem. A cold spot behind a sofa, at a thermal bridge, or on a chilled-water line will collect moisture even when the assembly's average performance looks fine. The calculator reports the surface temperature and dew point for exactly this reason.
• Radiation is not a high-temperature-only effect. At room temperature the radiative coefficient between surfaces is around 5 W/m²·K, comparable to natural convection. This is why a room with a large cold window feels cold at 21 °C, and why a radiant floor at 27 °C is comfortable.
• Emissivity has nothing to do with colour. White paint and black paint both radiate at about ε 0.9 in the infrared. Only bare metals are low, which is why a radiant barrier must be shiny foil facing an air space — and why it stops working when it gets dusty.
• This is steady-state conduction only. Real buildings also lose heat through air leakage, which frequently rivals conduction, and they store heat in their mass, which shifts loads in time. Treat these figures as the envelope conduction term of a load calculation, not as the whole load. A full design follows ACCA Manual J or the ASHRAE Handbook procedures.

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