To determine the concentration of biomolecules using a label-free optical biosensor, it is necessary to measure the serial signal from the reaction starting point, which is inconvenient for practical applications. Here, we propose an alternative detection method for determining the concentration of a biomolecule. The method, which is derived from the fraction bound equation of the Langmuir adsorption model, determines the concentration relative to a reference sample with required accuracy, with a single measurement at any point in time. We also experimentally demonstrated the method and its accuracy by detecting streptavidin-biotin complexes using on-chip optical sensors based on active disk resonators integrated with microfluidic circuits. By performing the proposed method in a simultaneous parallel measurement scheme, signal fluctuations evenly induced in the detectors by external perturbations could be automatically suppressed, similar to the balanced detection method. We expect our approach to be applicable to practical applications where fast and accurate detection responses are needed.