Smartphone video-based measurement of heart rate typically uses photoplethysmography (PPG). Prior accuracy studies report low mean absolute errors for apps based on contact PPG on a fingertip, but substantial errors on a troubling percentage of measurements. In this study, we aimed to reduce the rate of substantial heart rate estimation errors by introducing a novel signal present in fingertip videos: fingertip contact surface area. We propose a simplified model of the information captured in this area signal, by which we expect the area signal to covary with fingertip green color intensity. We utilize a dataset of 786 videos with corresponding reference heart rate measurements from 62 participants. We show how to measure the area signal from fingertip videos, and demonstrate that it does typically correlate positively with green color intensity. We estimate heart rate using two parallel algorithms, one based on the green color signal only and the other based on both green color intensity and fingertip contact surface area. We demonstrate lower rates of substantial errors using the second algorithm, compared both to our own first algorithm and to published accuracy results from commercial contact PPG-based apps. We conclude by proposing additional potential uses of this fingertip contact surface area signal to measure other medical parameters using smartphone fingertip videos.