Abstract We present measurements of the branching fractions for the decays B → Kμ + μ − and B → Ke + e − , and their ratio (R K ), using a data sample of 711 fb −1 that contains 772 × 106 B B ¯ $$ B\overline{B} $$ events. The data were collected at the ϒ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. The ratio R K is measured in five bins of dilepton invariant-mass-squared (q 2): q 2 ∈ (0.1, 4.0), (4.00, 8.12), (1.0, 6.0), (10.2, 12.8) and (> 14.18) GeV2 /c 4, along with the whole q 2 region. The R K value for q 2 ∈ (1.0, 6.0) GeV2 /c 4 is 1.03 − 0.24 + 0.28 $$ {1.03}_{-0.24}^{+0.28} $$ ± 0.01. The first and second uncertainties listed are statistical and systematic, respectively. All results for R K are consistent with Standard Model predictions. We also measure CP-averaged isospin asymmetries in the same q 2 bins. The results are consistent with a null asymmetry, with the largest difference of 2.6 standard deviations occurring for the q 2 ∈ (1.0, 6.0) GeV2 /c 4 bin in the mode with muon final states. The measured differential branching fractions, d ℬ $$ d\mathrm{\mathcal{B}} $$ /dq 2, are consistent with theoretical predictions for charged B decays, while the corresponding values are below the expectations for neutral B decays. We have also searched for lepton-flavor-violating B → Kμ ± e ∓ decays and set 90% confidence-level upper limits on the branching fraction in the range of 10 −8 for B + → K + μ ± e ∓, and B 0 → K 0 μ ± e ∓ modes.