<p>This paper establishes a quantitative calculation method for the strength of flocs under laminar shear force, where the key factors involved are the binding force and breaking force of flocs. The binding force of flocs is regarded as the floc strength, and the critical breaking force of flocs in laminar flow is considered a function of the shear rate (<i>γ</i>) and the area of flocs (<i>A</i>). The beaker experiments respectively explored the strength of flocs formed under different PAC dosages at a fixed stirring speed and different stirring speeds at a fixed dosage. It was discovered that the floc strength was the highest at a PAC dosage of 20&#xa0;mg/L, reaching 11.89 nN; when the stirring speed was 80 r/min, the floc strength was the highest, attaining 13.33 nN. Furthermore, correlation analysis between the fractal dimension of flocs and their strength revealed a strong positive correlation with a correlation coefficient above 0.90 (<i>p</i> = 0.01). Finally, an integrated analysis of floc size, fractal dimension, and strength demonstrated that the turbidity removal rate is mainly determined by the floc size and floc strength, with the floc strength playing a dominant role in most cases. These findings provide theoretical guidance for improving the settling performance of flocs and developing efficient coagulation processes.</p> Graphical abstract <p></p>