Alpha-particle radiopharmaceutical therapy (αRPT) is currently enjoying increasing attention as a viable alternative to chemotherapy for targeting of disseminated micrometastatic disease. In theory, αRPT can be personalized through pre-therapeutic imaging and dosimetry. However, in practice, given the particularities of α-particle emissions, a dosimetric methodology that accurately predicts the thresholds for organ toxicity has not been reported. This is in part due to the fact that the biological effects caused by α-particle radiation differ markedly from the effects caused by traditional external beam (photon or electron) radiation or β-particle emitting radiopharmaceuticals. The concept of relative biological effectiveness (RBE) is used to quantify the ratio of absorbed doses required to achieve a given biological response with alpha particles versus a reference radiation (typically a beta emitter or external beam radiation). However, as conventionally defined, the RBE varies as a function of absorbed dose and therefore a single RBE value is limited in its utility because it cannot be used to predict response over a wide range of absorbed doses. Therefore, efforts are underway to standardize bioeffect modeling for different fractionation schemes and dose rates for both nuclear medicine and external beam radiotherapy. Given the preponderant use of external beams of radiation compared to nuclear medicine in cancer therapy, the more clinically relevant quantity, the 2 Gy equieffective dose, EQD2(α/β), has recently been proposed by the ICRU. In concert with EQD2(α/β), we introduce a new, redefined RBE quantity, named RBE2(α/β), as the ratio of the two linear coefficients that characterize the α particle absorbed dose-response curve and the low-LET megavoltage photon 2 Gy fraction equieffective dose-response curve. The theoretical framework for the proposed new formalism is presented along with its application to experimental data obtained from irradiation of a breast cancer cell line. Radiobiological parameters are obtained using the linear quadratic model to fit cell survival data for MDA-MB-231 human breast cancer cells that were irradiated with either α particles or a single fraction of low-LET Cs γ rays. From these, the linear coefficient for both the biologically effective dose (BED) and the EQD2(α/β) response lines were derived for fractionated irradiation. The standard RBE calculation, using the traditional single fraction reference radiation, gave RBE values that ranged from 2.4 for a surviving fraction of 0.82-6.0 for a surviving fraction of 0.02, while the dose-independent RBE2(4.6) value was 4.5 for all surviving fraction values. Furthermore, bioeffect modeling with RBE2(α/β) and EQD2(α/β) demonstrated the capacity to predict the surviving fraction of cells irradiated with acute and fractionated low-LET radiation, α particles and chronic exponentially decreasing dose rates of low-LET radiation. RBE2(α/β) is independent of absorbed dose for α-particle emitters and it provides a more logical framework for data reporting and conversion to equieffective dose than the conventional dose-dependent definition of RBE. Moreover, it provides a much needed foundation for the ongoing development of an α-particle dosimetry paradigm and will facilitate the use of tolerance dose data available from external beam radiation therapy, thereby helping to develop αRPT as a single modality as well as for combination therapies.