It is known that the exhaust stream of internal combustion engines contains soot agglomerates with fractal geometries. The samples of real soot agglomerates can only be analyzed from projections observed with powerful microscopes. The fractal dimension of an agglomerate is estimated from the combination of its volume and a characteristic radius. The radius of gyration is often considered as the characteristic radius and, in case of being composed of uniform primary particles, the volume of the agglomerate can be represented by the number of primary particles. However, none of them (radius of gyration or number of primary particles) can be determined from projected images. As previous works have pointed out, there is an intrinsic error in the estimation of the real radius of gyration, which cannot be measured directly from the microscopy projected images. In this work, an algorithm is proposed to generate three-dimensional synthetic agglomerates that mimic the fractal geometry of real ones. The real three-dimensional radius of gyration is measured and compared to the one found from projections. Also, the number of primary particles is compared to that estimated from the projected area. The consequence of both estimation errors on the determination of the fractal dimension is analyzed. It is shown that the fractal dimension is overestimated when it is calculated from projected images. (C) 2017 Elsevier B.V. All rights reserved.