Let X be a ball quasi-Banach function space on Rn. In this article, under some mild assumptions about both X and the boundedness of the Hardy–Littlewood maximal operator on the associate space of the convexification of X, the authors prove that, for any f∈(X/R)∩⋃s∈(0,1)W˙Xs,q(Rn),‖f‖X/R≲lim infs→0+s1q‖[∫Rn|f(⋅)−f(y)|q|⋅−y|n+sqdy]1q‖X≤lim sups→0+s1q‖[∫Rn|f(⋅)−f(y)|q|⋅−y|n+sqdy]1q‖X≲‖f‖X/R and, for any γ∈R∖{0} and f∈X/R,supλ∈(0,∞)λ‖[∫Rn1Ef(λ,q,γ)(⋅,y)|⋅−y|γ−ndy]1q‖X∼‖f‖X/R with the positive equivalence constants independent of f, where f∈X/R if and only if there exists a∈R such that f+a∈X and where ‖f‖X/R:=infa∈R‖f+a‖X<∞, the index q∈(0,∞) is related to X, W˙Xs,q(Rn) is the homogeneous fractional Sobolev space associated with the ball quasi-Banach function space X, andEf(λ,q,γ):={(x,y)∈Rn×Rn:|f(x)−f(y)|>λ|x−y|γq}. In the case when X:=Lp(Rn) with 1≤q=p<∞ and f∈X, the first formula is closely related to the celebrated classical formula of V. Maz'ya and T. Shaposhnikova and the second formula is exactly the recent formula of H. Brezis et al. These results are new even when X=Lp(Rn) with 1≤q<p<∞ and 0<q≤p<1. All these results are of quite wide generality and, even when they are applied to various specific function spaces, most of the obtained results are new. To obtain these results, the authors overcome those obstacles caused by the deficiency of both the translation invariance and an explicit expression of the quasi-norm of X under consideration via establishing some weighted estimates and new decompositions, which depend on the extrapolation and the exact operator norm of the Hardy–Littlewood maximal operator.