  The $\eta \to 3 \pi$ amplitude is sensitive to the quark mass difference
$m_u-m_d$ and offers a unique way to determine the quark mass ratio $Q^2 \equiv
(m_s^2-m_{ud}^2)/(m_d^2-m_u^2)$ from experiment. We calculate the amplitude
dispersively and fit the KLOE data on the charged mode, varying the subtraction
constants in the range allowed by chiral perturbation theory. The
parameter-free predictions obtained for the neutral Dalitz plot and the
neutral-to-charged branching ratio are in excellent agreement with experiment.
Our representation of the transition amplitude implies $Q = 22.0 \pm 0.7$.
