Quantitative analysis of human gait is critical for early discovery, progressive tracking, and rehabilitation of neurological and musculoskeletal disorders, such as Parkinson’s Disease, stroke, and Cerebral Palsy. Gait analysis typically involves estimating gait characteristics, such as spatio-temporal gait parameters and gait health indicators (e.g., step time, length, symmetry, and balance). Traditional methods of gait analysis involve the use of cameras, wearables, and force plates, but are limited in operational requirements when applied in daily life - such as direct line-of-sight, carrying devices, and dense deployment. This paper introduces a novel approach for gait analysis by passively sensing footstep-induced floor vibrations during walking using vibration sensors mounted on the floor surface. Our approach is non-intrusive, scalable, and perceived as more privacy-friendly, making it suitable for continuous gait health monitoring in daily life. We developed a floor vibration-based gait analysis framework to estimate various gait parameters that are used as standard metrics in medical practices, including temporal parameters (step, stride, stance, swing, double-support, single-support time) and spatial parameters (step length, width, angle, stride length), and extracts gait health indicators (cadence/walking speed, left-right symmetry, gait balance, initial contact types). The main challenge is that floor vibrations are distinct across different floor types. To address this challenge, our approach develops floor-adaptive algorithms to extract floor-specific features and is designed to be generalizable to various settings, including homes, hospitals, and eldercare facilities. We evaluate our approach through real-world walking experiments with 20 adults with 12,231 labeled gait cycles across concrete and wooden floors. Our results show 90.5% (RMSE 0.08s), 71.3% (RMSE 0.38m), and 92.3% (RMSPE 7.7%) accuracy in estimating temporal, spatial parameters, and gait health indicators, respectively.