The angular distribution and differential branching fraction of the decay B +→ K + μ + μ − are studied with a dataset corresponding to 1.0fb−1 of integrated luminosity, collected by the LHCb experiment. The angular distribution is measured in bins of dimuon invariant mass squared and found to be consistent with Standard Model expectations. Integrating the differential branching fraction over the full dimuon invariant mass range yields a total branching fraction of B (B + → K + μ + μ −) = (4.36 ± 0.15 ± 0.18) × 10−7. These measurements are the most precise to date of the B + → K + μ + μ − decay.