We determine the sensitivity to neutrino oscillation parameters from a study of atmospheric neutrinos in a magnetised detector such as the ICAL at the proposed India-based Neutrino Observatory. In such a detector, which can separately count ν μ and ν μ -induced events, the relatively smaller (about 5%) uncertainties on the neutrinoantineutrino flux ratios translate to a constraint in the χ 2 analysis that results in a significant improvement in the precision with which neutrino oscillation parameters such as sin 2 θ 23 can be determined. Such an effect is unique to all magnetisable detectors and constitutes a great advantage in determining neutrino oscillation parameters using such detectors. Such a study has been performed for the first time here. Along with an increase in the kinematic range compared to earlier analyses, this results in sensitivities to oscillation parameters in the 2-3 sector that are comparable to or better than those from accelerator experiments where the fluxes are significantly higher. For example, the 1σ precisions on sin 2 θ 23 and | m 2 32(31) | achievable for 500 kton year exposure of ICAL are ∼9 and ∼2.5%, respectively, for both normal and inverted hierarchies. The mass hierarchy sensitivity achievable with this combination when the true hierarchy is normal (inverted) for the same exposure is χ 2 ≈ 8.5 ( χ 2 ≈ 9.5).