The main result is the following concentration of mass inequality for isotropic convex bodies. Let \(K\) be an isotropic convex body in \(\mathbb{R}^n\) with isotropic constant \(L_K\). Then \(\text{Prob}(\{x\in K : \| x\|_2 \geq c\sqrt{n} L_K t\}) \leq \exp(-\sqrt{n} t)\) for all \(t\geq 1\), where \(c>0\) is an absolute constant. This was shown previously for \(1\)-unconditional isotropic bodies by S. Bobkov and A. Koldobsky [Lect. Notes Math. 1807, 44–52 (2003; Zbl 1039.52003)] and sharpens a concentration estimate of S. Alesker [Oper. Theory, Adv. Appl. 77, 1–4 (1995; Zbl 0834.52004)]. In fact a more general estimate is proved for any convex body \(K\) in terms of the operator taking \(K\) to isotropic position, which shows that the above concentration estimate is stable. The proofs use the \(L_q\)-norms and \(L_q\)-centroid bodies associated to a convex body.