We consider the evaluation of the Number of Degrees of Freedom (NDF) of the field radiated by square sources in the far zone. The analysis is performed by employing a Singular-Value Decomposition (SVD) of the radiation operator in the two-dimensional scalar case. To this end, we start the analysis from simple geometries like two parallel strips and angle strips where analytical results can be established. For sufficiently spaced strip sources, the NDF depends only on their total electrical length. Then results for square sources follow on the same line. Finally, the numerical investigation of the case of concentric square sources, leading to an NDF independent on the inner source, opens the way to the discussion of the NDF of a full square source. In this case, it results that it depends only on the source perimeter.