Accurate camera motion estimation is critical to estimate human motion in the global space. A standard and widely used method for estimating camera motion is Simultaneous Localization and Mapping (SLAM). However, SLAM only provides a trajectory up to an unknown scale factor. Different from previous attempts that optimize the scale factor, this paper presents Optimization-free Camera Motion Scale Calibration (OfCaM), a novel framework that utilizes prior knowledge from human mesh recovery (HMR) models to directly calibrate the unknown scale factor. Specifically, OfCaM leverages the absolute depth of human-background contact joints from HMR predictions as a calibration reference, enabling the precise recovery of SLAM camera trajectory scale in global space. With this correctly scaled camera motion and HMR's local motion predictions, we achieve more accurate global human motion estimation. To compensate for scenes where we detect SLAM failure, we adopt a local-to-global motion mapping to fuse with previously derived motion to enhance robustness. Simple yet powerful, our method sets a new standard for global human mesh estimation tasks, reducing global human motion error by 60% over the prior SOTA while also demanding orders of magnitude less inference time compared with optimization-based methods.