Age-Differentiated Accessibility and Spatial Equity of Urban Fitness Facilities: Implications for Socially Sustainable Neighbourhood Planning in Central Harbin, China

Equitable access to health-promoting public services is an important component of socially sustainable urban development, yet fitness-facility accessibility is often assessed under homogeneous demand assumptions. This study develops an age-differentiated framework for central Harbin, China, integrating 100 m age-stratified population data, facility functional area, pedestrian-network travel costs, and physical-activity participation rates within an MGH-3SFCA model. Accessibility was evaluated for four age groups at 15 min, with shorter-threshold comparisons, population exposure analysis, bivariate LISA, and sensitivity tests. Adults and students generally formed the relatively higher-accessibility pair, whereas children and seniors remained more disadvantaged. More than 91% of each age group was located in zero, very low, or low accessibility classes. High-intensity ball-sports facilities were dominated by geographic non-coverage, while resistance-training facilities were more widely reachable but mostly at very low levels. The adult–senior zero-accessibility population gap widened from 3.52 percentage points at 15 min to 13.66 at 5 min. High–Low clusters occupied only 5.90–7.39% of land grids but contained 11.77–13.25% of corresponding populations. Broad spatial patterns were stable to alternative composite weighting, while some age contrasts were specification-dependent. The framework supports age-responsive and socially sustainable neighbourhood planning by distinguishing spatial coverage, population exposure, and potential local mismatch.