Goal: The countermovement jump (CMJ) is commonly used to measure the explosive power of the lower body. This study evaluates how accurately markerless motion capture (MMC) with a single smartphone can measure bilateral and unilateral CMJ jump height. Methods: First, three repetitions each of bilateral and unilateral CMJ were performed by sixteen healthy adults (mean age: 30.87 $\pm$ 7.24 years; mean BMI: 23.14 $\pm$ 2.55 $kg/m^2$) on force plates and simultaneously captured using optical motion capture (OMC) and one smartphone camera. Next, MMC was performed on the smartphone videos using OpenPose. Then, we evaluated MMC in quantifying jump height using the force plate and OMC as ground truths. Results: MMC quantifies jump heights with MAE between 1.47 and 2.82 cm, and ICC between 0.84 and 0.99 without manual segmentation and camera calibration. Conclusions: Our results suggest that using a single smartphone for markerless motion capture is feasible. Index Terms - Countermovement jump, Markerless motion capture, Optical motion capture, Jump height. Impact Statement - Countermovement jump height can be accurately quantified using markerless motion capture with a single smartphone, with a simple setup that requires neither camera calibration nor manual segmentation.