Rotary ultrasonic grinding machining (RUGM) has been employed in Si3N4 ceramics parts machining widely, and the surface morphology is related with surface friction and wear properties directly. It is necessary to investigation on the surface morphology characterization to improve surface quality. Surface morphology of Si3N4 ceramics for rotary ultrasonic grinding machining was investigated based on fractal theory in the paper. The fractal features of surface morphology have been proved with qualitative and quantitative investigation. Differential box-counting method and peleg-blanket method was applied to calculate fractal dimension, but low calculation accuracy was found. So a new fractal dimension calculation method called perimeter-volume method has been proposed. The results show that the calculation deviation rate of morphology fractal dimension is only 2.5%. Meanwhile, the influence of spindle speed, cutting depth, feed rate and cutting force on fractal dimension has also been investigated. The investigation results provide the support for surface morphology optimization. (C) 2016 Elsevier B.V. All rights reserved.