Estimating parameters of clinical significance, like coronary stenosis, accurately and precisely from cardiac CT images remains a difficult task as image noise and cardiac motion can degrade image quality and distort underlying anatomic information. The purpose of this study was to develop a computational framework to objectively quantify stenosis estimation task performance of an ideal estimator in cardiac CT. The resulting scalar figure-of-merit, the estimability index (e’), serves as a cardiac CT specific task-based measure of image quality. The developed computational framework consisted of idealized coronary vessel and plaque models, asymmetric motion point spread functions (mPSF), CT image blur (MTF) and noise operators (NPS), and an automated maximum-likelihood estimator (MLE) implemented as a matched template squared-difference operator. Using this framework, e’ values were calculated for 131 clinical case scenarios from the Prospective Multicenter Imaging Study for Evaluation of Chest Pain (PROMISE) trial. The calculated e’ results were then utilized to classify patient cases into two exclusive cohorts, high-quality and low-quality, characterized by clinically meaningful differences in image quality. An e’ based linear classifier categorized the 131 patient datasets with an AUC of 0.96 (6 false-positives and 10 false-negatives), compared to an AUC of 0.89 (4 false-positives and 20 false-negatives) for a linear classifier based on contrast-to-noise ratio (CNR). In summary, a computational framework to objectively quantify stenosis estimation task performance was successfully implemented and was reflective of clinical results in the context of subset of a large clinical trial (PROMISE) with diverse sites, readers, scanners, acquisition protocols, and patient types.