We use the 2 per cent distance measurement from our reconstructed baryon acoustic oscillations (BAOs) signature using the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) luminous red galaxies from Padmanabhan et al. and Xu et al. combined with cosmic microwave background data from Wilkinson Microwave Anisotropy Probe (WMAP7) to measure parameters for various cosmological models. We find a 1.7 per cent measurement of H0 = 69.8 ± 1.2 km s−1 Mpc−1 and a 5.0 per cent measurement of for a flat universe with a cosmological constant. These measurements of H0 and Ωm are robust against a range of underlying models for the expansion history. We measure the dark energy equation of state parameter w = −0.97 ± 0.17, which is consistent with a cosmological constant. If curvature is allowed to vary, we find that the Universe is consistent with a flat geometry (ΩK = −0.004 ± 0.005). We also use a combination of the 6 Degree Field Galaxy Survey BAO data, WiggleZ Dark Energy Survey data, Type Ia supernovae data and a local measurement of the Hubble constant to explore cosmological models with more parameters. Finally, we explore the effect of varying the energy density of relativistic particles on the measurement of H0.