A method that can robustly estimate the distance to a foregoing vehicle with a monocular camera is in high demand for developing inexpensive Adaptive Cruise Control (ACC) systems. The accuracy of the estimated distances heavily depends on the road geometry and the true distance to the target vehicle. That motivates us to develop a distance estimation method that has two important properties: (a) it can deal with non-planar road surfaces from the first principle, and (b) it can estimate not only the distance but its variance of the error through mathematical analyses. Experiments on the KITTI dataset demonstrated that the proposed distance estimator is more robust and stable than the planar assumption model, and we verified by Monte Carlo simulations that our error model correctly predicts the variance of the error in the estimated distances.