We quantify how demand shocks propagate across exchange rates in an interconnected FX market. Using 11 years of daily customer-bank FX flows and exchange-rate returns across 17 currencies, we show that cross-currency propagation can be decomposed into factor-level repricing and currencies' exposures to common risks. To make this decomposition empirically tractable, we identify three traded risk factors that account for 90% of the non-diversifiable risk banks bear when absorbing customer demand imbalances and that plausibly exhibit no cross-factor price effects. We estimate each factor's price sensitivity using sovereign bond auction announcements as instruments for non-informational shocks to factor demand and find that the FX market is highly elastic. Mapping factor-level price sensitivities back to currencies, we find that a $1 billion demand shock to one currency moves other exchange rates by up to 9 basis points. Propagation is strongest among currencies with same-signed factor exposures and weaker when exposures offset. Consistent with the model-implied propagation patterns, out-of-sample FX interventions show that shocks originating in one currency transmit broadly across FX markets through shared risk exposures.