We introduce a fast method to measure the conversion gain in complementary metal-oxide-semiconductor active pixel sensors, which accounts for nonlinearity and interpixel capacitance (IPC). The standard mean-variance method is biased because it assumes that pixel values depend linearly on the signal, and existing methods to correct for nonlinearity still introduce significant biases. While current IPC correction methods are prohibitively slow for a per-pixel application, our new method uses separate measurements of the IPC kernel to calculate the gain almost instantaneously. Using test data from a flight detector of the ESA Euclid mission, the IPC correction recovers the results of slower methods with 0.1% accuracy. The nonlinearity correction ensures that the estimated gain is independent of signal, correcting a bias of more than 2.5%.