The low-contrast detectability of computed tomography (CT) images is commonly evaluated by the contrast-to-noise ratio (CNR) because of its convenience to measure. However, the correlation between CNR and visual detectability is poor because the CNR is a simple index determined by both the contrast of the object and the standard deviation of the image noise. On the other hand, the signal-to-noise ratio (SNR), especially SNR based on the statistical decision theory model (SNR_{S, D}) and SNR based on the matched-filter model (SNR_M) are considered superior to CNR. In this study, we investigated a new physical image quality index for evaluating low-contrast detectability (SNR_A), which is approximately derived from SNR_{S, D} and SNR_M. The new index, which was calculated using the object size, contrast of the object and the noise power spectrum, provided good approximations when the diameter of the rod object was equal and >5 mm. The diameter dependency of the SNR_A was also found to provide better sensitivity than the sensitivities of CNR and object-specific CNR, similar to SNR_{S, D} and SNR_M. The results suggested that the proposed convenient index should be useful for evaluating the low-contrast detectability of CT images.