Filter radiometers are used to measure the thermodynamic temperature of a blackbody source by determining the radiance of the source over a spectral region defined by the filter. This paper presents a method to calculate the uncertainty from the measurement equation directly. The calculation of the uncertainty associated with these temperature results is complicated by the significant correlations between different wavelength values of the spectral responsivity of the radiometer. It not only provides sufficient generality to include full covariance information, but is also written as a step-by-step guide for users on how to do the necessary calculations in either a spreadsheet package or a matrix-based programming language.