A cylindrical graphite ionization chamber of sensitive volume 1002.4 cm³ was designed and fabricated at Bhabha Atomic Research Centre (BARC) for use as a reference dosimeter to measure the strength of high dose rate (HDR) ¹⁹²Ir brachytherapy sources. The air kerma calibration coefficient (N-K) of this ionization chamber was estimated analytically using Burlin general cavity theory and by the Monte Carlo method. In the analytical method, calibration coefficients were calculated for each spectral line of an HDR ¹⁹²Ir source and the weighted mean was taken as N_K. In the Monte Carlo method, the geometry of the measurement setup and physics related input data of the HDR ¹⁹²Ir source and the surrounding material were simulated using the Monte Carlo N-particle code. The total photon energy fluence was used to arrive at the reference air kerma rate (RAKR) using mass energy absorption coefficients. The energy deposition rates were used to simulate the value of charge rate in the ionization chamber and N_K was determined. The Monte Carlo calculated N_K agreed within 1.77% of that obtained using the analytical method. The experimentally determined RAKR of HDR ¹⁹²Ir sources, using this reference ionization chamber by applying the analytically estimated N-K, was found to be in agreement with the vendor quoted RAKR within 1.43%.