Current urban development policies prioritize active accessibility (walking and cycling) to reduce car dependence and improve sustainability. The 15-minute city concept emphasizes proximity to essential destinations within a 15-minute walk or cycle. However, this concept has limitations: defining 'relevant' opportunities varies among individuals; acceptable travel time depends on the destination; and walking time perception is inaccurate. This research addresses these limitations by focusing on accessibility to various destination types, using cumulative opportunities (Total Destinations) and Variety (number of different opportunity types) as accessibility indicators within a 15-minute threshold. The study aims to compare active accessibility and its inequality across European cities, filling a gap in existing research which primarily focuses on individual cities or uses different transport modes or geographical scales.

Several studies have measured active accessibility within individual cities, generally finding that city centers are most accessible. However, comparisons of active accessibility across cities in different countries and assessments of inequalities are lacking. Methodologies like Walk Score exclude many European countries, and OSM-WALK-EU, while applicable to Europe, is not easily scalable to large datasets. Existing between-city comparisons often focus on job accessibility using various transport modes or broader service access using road networks, not solely pedestrian accessibility. This study aims to address these gaps by providing a comprehensive cross-city comparison of pedestrian accessibility and its associated inequality in Europe.

The study analyzed 585 European cities with populations over 100,000, using open-source data and software. Administrative boundaries were from Eurostat/GISCO, population data from Eurostat, and street networks from OpenStreetMap. The pedestrian network was extracted using the Pandana library, excluding non-walkable segments. Accessibility was measured using two indicators: Total Destinations (cumulative opportunities) and Variety (number of different destination types). Ten destination types were classified (education, supermarkets, healthcare, etc.). Accessibility was calculated for all network nodes using a cumulative opportunities measure with three walking speeds (0.7 m/s, 0.9 m/s, and 1.1 m/s) to account for varying walking speeds, and the mean value was used for each location. Results were represented on a hexagon grid (H3 level 10) covering each city. Inequality was measured using pseudo-Gini coefficients: Territorial-based Gini (T-Gini) considering all hexagons, and Population-based Gini (P-Gini) weighting hexagons by population density. Analysis included descriptive statistics, correlation analysis, and comparisons across population size and density classes.

Results showed considerable variation in pedestrian accessibility across European cities and countries. At the country level, mean Total Destinations ranged from 17.5 (Sweden) to 136.4 (Switzerland). At the city level, Total Destinations ranged widely (3.3–593.4), with a positively skewed distribution. Variety scores were more normally distributed (1.18–9.90), with a mean of 5.91. Within-city analysis of a sample of 12 cities revealed that Total Destinations tended to cluster in city centers, while Variety showed more polycentric patterns. An exponential decay upward relationship existed between Total Destinations and Variety, indicating diminishing returns. Population density showed a linear relationship with Total Destinations and an exponential decay upward relationship with Variety, suggesting diminishing returns beyond a certain density (around 75 inhabitants/ha). Inequality analysis showed that P-Gini coefficients were consistently lower than T-Gini coefficients for both indicators, indicating that residential location choices partially alleviate inequality. Variety inequality was systematically lower than Total Destinations inequality. Larger cities exhibited lower inequality levels.

The findings highlight the diversity of pedestrian accessibility conditions across European cities. While Total Destinations is useful for within-city comparisons, Variety provides a more effective measure for both within-city and between-city comparisons. The exponential decay relationship between Total Destinations and Variety suggests that increasing the number of destinations doesn't necessarily enhance diversity. The diminishing returns of density on Variety indicate that other factors influence accessibility, highlighting the importance of urban structure and local economy. The lower P-Gini compared to T-Gini values suggests that residential location decisions mitigate inequality, particularly concerning Variety. The more polycentric pattern associated with Variety points to the importance of fostering diverse centralities to achieve equal access to different opportunity types. The study's findings support the 15-minute city concept by emphasizing the importance of increasing the diversity of accessible opportunities rather than solely focusing on the total number.

This research demonstrates the heterogeneity of pedestrian accessibility in European cities and highlights the importance of considering both the total number and variety of accessible destinations. The study emphasizes the need for urban planning strategies that promote diverse centralities and improve pedestrian infrastructure to enhance accessibility and reduce inequalities. Future research could explore the use of multiple accessibility thresholds, incorporate cycling accessibility, and expand the geographical scope to include cities beyond Europe.

The study's limitations include the use of a single accessibility threshold (15 minutes), the assumption of constant walking speeds, potential incompleteness of OpenStreetMap data, inconsistencies in city delimitation across countries, and the exclusion of micro-scale pedestrian network features. These limitations suggest that the results should be interpreted as representing potential rather than actual accessibility.