We have developed a physical model for the spectral irradiance of $1\mathrm{kW}$ tungsten halogen incandescent lamps for the wavelength range $340–850\mathrm{nm}$ . The model consists of the Planck’s radiation law, published values for the emissivity of tungsten, and a residual spectral correction function taking into account unknown factors of the lamp. The correction function was determined by measuring the spectra of a 1000 W, quartz-halogen, tungsten coiled filament (FEL) lamp at different temperatures. The new model was tested with lamps of types FEL and 1000 W, 120 V quartz halogen (DXW). Comparisons with measurements of two national standards laboratories indicate that the model can account for the spectral irradiance values of lamps with an agreement better than 1% throughout the spectral region studied. We further demonstrate that the spectral irradiance of a lamp can be predicted with an expanded uncertainty of 2.6% if the color temperature and illuminance values for the lamp are known with expanded uncertainties of $20\mathrm{K}$ and 2%, respectively. In addition, it is suggested that the spectral irradiance may be derived from resistance measurements of the filament with lamp on and off.