We prove that for the Ising model defined on the plane $$\mathbb Z ^2$$ Z 2 at $$\beta \,{=}\,\beta _c,$$ β = β c , the average magnetization under an external magnetic field $$h>0$$ h > 0 behaves exactly like $$\begin{aligned} \langle \sigma _0\rangle _{\beta _c, h} \asymp h^{\frac{1}{15}}. \end{aligned}$$ 〈 σ 0 〉 β c , h ≍ h 1 15 . The proof, which is surprisingly simple compared to an analogous result for percolation [i.e. that $$\theta (p)=(p-p_c)^{5/36+o(1)}$$ θ ( p ) = ( p - p c ) 5 / 36 + o ( 1 ) on the triangular lattice (Kesten in Commun Math Phys 109(1):109–156, 1987; Smirnov and Werner in Math Res Lett 8(5–6):729–744, 2001)] relies on the GHS inequality as well as the RSW theorem for FK percolation from Duminil-Copin et al. (Commun Pure Appl Math 64:1165–1198, 2011). The use of GHS to obtain inequalities involving critical exponents is not new; in this paper we show how it can be combined with RSW to obtain matching upper and lower bounds for the average magnetization.