We analyzed the thermal emission from the entire surface of the millisecond pulsar PSR J0437–4715 observed in the ultraviolet and soft X–ray bands . For this , we calculated non-magnetized , partially ionized atmosphere models of hydrogen , helium , and iron compositions and included plasma frequency effects that may affect the emergent spectrum . This is particularly true for the coldest atmospheres composed of iron ( up to a few percent changes in the soft X–ray flux ) . Employing a Markov chain Monte Carlo method , we found that the spectral fits favour a hydrogen atmosphere , disfavour a helium composition and rule out iron atmosphere and blackbody models . By using a Gaussian prior on the dust extinction , based on the latest 3D map of Galactic dust , and accounting for the presence of hot polar caps found in previous work , we found that the hydrogen atmosphere model results in a well-constrained neutron star radius \mbox { $R _ { NS } $ } = 13.6 ^ { +0.9 } _ { -0.8 } \hbox { $ { km } $ } and bulk surface temperature \mbox { $T _ { eff } ^ { \infty } $ } = \left ( 2.3 \pm 0.1 \right ) \mbox { $ \times 10 ^ { 5 } $ } % \hbox { $ { K } $ } . This relatively large radius favours a stiff equation of state and disfavours a strange quark composition inside neutron stars .