The capacitance of 24° tilt calcium doped Y1−xCaxBa2Cu3O7−δ grain boundaries has been measured for thin films with x in the range 0.0–0.3. The capacitance was determined from the hysteresis in the I-V characteristic. By measuring the capacitance as a function of the voltage across the junctions it was possible to observe the contribution of both parasitic substrate capacitance and heating to the hysteresis. These effects enable the determination of the intrinsic capacitance of the grain boundaries. The effect of thermal noise on the measurement is also assessed, and found to be much less than the observed changes in the capacitance. The capacitance is found to increase as the calcium doping increases: from 0.2Fm−2 for x=0.0 to a maximum of 1.2Fm−2 for x=0.3. The changes in the capacitance per unit area are observed to be inversely proportional to the corresponding changes in the resistance area product.