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Let $\mathcal{C}$ be a length-category. Generalizing the Loewy length, we propose the layer length associated with a torsion theory, which is a new measure for objects of $\mathcal{C}$. As an application, we use the layer lengths and the Igusa-Todorov function to get a theorem (see Theorem 6.4) having as corollaries the main results of Huard et al. (Bull Lond Math Soc 41:367-376, ) and Wang (Commun Algebra 22(7):419-449, ). [ABSTRACT FROM AUTHOR]