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We present a novel fitting formula for the halo concentration enhancement inchameleon $f(R)$ gravity relative to General Relativity (GR). The formula isderived by employing a large set of $N$-body simulations of the Hu-Sawicki$f(R)$ model which cover a wide range of model and cosmological parameters,resolutions and simulation box sizes. The complicated dependence of theconcentration on halo mass $M$, redshift $z$, and the $f(R)$ and cosmologicalparameters can be combined into a simpler form that depends only on a rescaledmass $M/10^{p_2}$, with$p_2\equiv1.5\log_{10}\left[|{\bar{f}_R(z)}|/(1+z)\right]+21.64$ and$\bar{f}_R(z)$ the background scalar field at $z$, irrespective of the $f(R)$model parameter. Our fitting formula can describe the concentration enhancementwell for redshifts $z\leq3$, nearly 7 orders of magnitude in $M/10^{p_2}$ andfive decades in halo mass. This is part of a series of works which aims toprovide a general framework for self-consistent and unbiased tests of gravityusing present and upcoming galaxy cluster surveys. The fitting formula, whichis the first quantitative model for the concentration enhancement due tochameleon type modified gravity, is an important part in this framework andwill allow continuous exploration of the parameter space. It can also be usedto model other statistics such as the matter power spectrum.

A general framework to test gravity using galaxy clusters II: A universal model for the halo concentration in $f(R)$ gravity