How the calculator works
Each pane is described by its spectral transmittance \(T(\lambda)\) and front and back reflectance \(R_f(\lambda)\), \(R_b(\lambda)\) from 300 to 2500 nm. Panes are combined with the net-radiation (multiple-reflection) method, which tracks light bouncing between every pair of surfaces. For two panes,
and the same bookkeeping gives the fraction of sunlight absorbed in each pane. Visible transmittance and reflectance are weighted by the CIE D65 illuminant and the photopic eye response \(V(\lambda)\) from 380 to 780 nm. Solar values are weighted by the ASTM G173 AM1.5 direct-plus-circumsolar spectrum from 300 to 2500 nm, about 53 % of which is visible. Color is CIELAB under D65 with the 1931 2° observer.
Generic glass and low-e coatings
Generic panes use a soda-lime glass model: a refractive index near 1.52 and an absorption spectrum set by iron. Ferrous iron (Fe²⁺) absorbs a broad band centered near 1050 nm, which gives clear glass its green edge and cuts near-infrared transmission; ferric iron and the silicate network absorb in the ultraviolet. Low-iron glass has about a tenth of the iron. The model reproduces typical published values, such as 89 % visible and about 80 % solar transmittance for 6 mm clear float and 91 % and 90 % for 6 mm low-iron glass.
The four generic coatings represent the main low-e families: a pyrolytic (hard-coat) tin oxide with an emissivity near 0.15, and sputtered single-, double-, and triple-silver stacks with emissivities of about 0.04, 0.025, and 0.015. Each adds silver's sharp rise in near-infrared reflectance. More silver layers mean a steeper edge, so less solar heat passes for the same visible light. The emissivity of the coated surface sets the radiative heat transfer across the gap. Real products vary, so use measured spectra for a specific product.
Surface numbering. Surfaces are numbered from the outside: a double-pane unit has surfaces #1 (outdoor face) through #4 (indoor face). In heating-dominated climates a low-e coating on #3 keeps more solar gain; in cooling climates a coating on #2 rejects more solar heat. Both give about the same U-factor.
Heat transfer and U-factor
The thermal model follows the ISO 15099 center-of-glass method used by NFRC and LBNL WINDOW. Each surface has its own temperature, and the model iterates until the energy balance closes. Heat crosses each gap by radiation between the two facing surfaces,
and by conduction and convection of the fill gas, using the ISO 15099 vertical-cavity Nusselt correlations with temperature-dependent properties of air, argon, krypton, and xenon. The 90 % fills are mixed with air by mole fraction. A vacuum gap has no gas conduction, so heat crosses only by radiation and through the support pillars. For a square array of pillars of radius \(a\) and spacing \(\lambda\), their conductance is about \(2k_\text{glass}a/\lambda^2\) (Collins and Simko).
The U-factor uses NFRC 100 winter conditions: −18 °C outside with 5.5 m/s wind, 21 °C inside, no sun. SHGC uses NFRC 200 summer conditions: 32 °C outside, 24 °C inside, 783 W/m² of sun. SHGC is the solar transmittance plus the inward-flowing fraction of the sunlight absorbed in the panes.
Assumptions and limits
- Center-of-glass values only. Whole-window ratings include the frame and the edge spacer, which raise the U-factor by roughly 10–30 % for a typical residential window.
- Generic layers are representative, typically within a few percent of real products. Use measured spectra for product selection or code compliance.
- Specular, uncoated-gap optics. Laminated glass interlayers, frits, films, and shades are not modeled.
- Gas fills are ideal mixtures at atmospheric pressure. Vacuum gaps neglect residual gas conduction, which is small below about 0.1 Pa.
References
- ISO 15099:2003, Thermal performance of windows, doors and shading devices — Detailed calculations.
- NFRC 100 (U-factor), NFRC 200 (SHGC and VT), and NFRC 300 (optical properties) procedures.
- ISO 9050:2003, Glass in building — Determination of light transmittance, solar direct transmittance, total solar energy transmittance, ultraviolet transmittance and related glazing factors.
- M. Rubin, “Optical properties of soda lime silica glasses,” Solar Energy Materials 12, 275–288 (1985).
- R. E. Collins and T. M. Simko, “Current status of the science and technology of vacuum glazing,” Solar Energy 62, 189–213 (1998).
- ASTM G173-03 reference solar spectra (NREL); CIE D65, V(λ), and 1931 colour-matching functions (CIE).
- Lawrence Berkeley National Laboratory, WINDOW and the International Glazing Database, the reference tools for this calculation.