Abstract The scaling behaviour of finite size ferromagnets is studied using an L dependent renormalization group, L being the characteristic “size” of the system, and a set of L dependent renormalization schemes. A new scaling formulation based on the scaling variable L/ξL is obtained in distinction to standard finite size scaling which is based on the variable L/ξ∞; ξL and ξ∞ being the correlation lengths in the finite system and the bulk, respectively. This new formulation reduces to the standard one when the only IR fixed point is the bulk one and/or in the limit (L/ξL)→∞, ξL→∞. When the finite system exhibits critical behaviour, then near the reduced fixed point (L/ξL)∼tv′L whereas near the bulk fixed point (L/ξ L)∼tvL, where v′ and v are the reduced and bulk correlation length exponents and t = T−Tc(L). Explicit calculations for an Ising system on S1×R3−ϵ(0⩽ϵ⩽1) are given to verify these assertions.