"Experts generally conclude that typical transit riders will walk up to a quarter-mile to a bus stop and a half-mile to a train station," Land Use Impacts on Transport - How Land Use Factors Affect Travel Behavior, 15 April 2011, Todd Litman, Victoria Transport Policy Institute With Rowan Steele
"Reasonable walking distance can vary, based on such factors as topography, sense of safety and security, and presence of interesting activity along the route of walking, but it is generally understood that most people will walk from 5 to 15 minutes to get to or from a transit station stop.
This walk time corresponds to approximately 1/4 mile to 1/2 mile.
The transit planning area should initially be defined based on walking distances of approximately 1/4 to 1/2 mile." Transportation Research Board PLANNING FOR TRANSIT-FRIENDLY LAND-USE. A HANDBOOK FOR NEW JERSEY COMMUNITIES 1994-96
"Findings show that sites within one-quarter mile of a rail station have significantly higher rates of transit use than sites between one-quarter and one-half mile from stations. Transit use drops even further one-half mile from stations." Transit Use and Proximity to Rail: Results from Large Employment Sites in the San Francisco, California, Bay Area Journal Transportation Research Record: Journal of the Transportation Research Board
"The 1983 National Personal Transportation Survey found that 70 percent of Americans will walk 500 feet for normal daily trips, 40 percent are willing to walk 1,000 feet, and 10 percent are willing to walk a half mile (U.S. DOT, 1986). In a study of travel behavior for nonwork trips, Hedel and Vance found that each additional walking minute to public transportation increases the probability of car use by 0.022 and kilometers driven by 0.15 per day (Hedel and Vance, 2006)." The Broader Connection between Public Transportation, Energy Conservation and Greenhouse Gas Reduction, Linda Bailey, Patricia L. Mokhtarian, Ph.D., Andrew Little
"The optimal walking distance between a transit station or stop and a place of employment is 500 to 1,000 feet. Residents are willing to walk slightly longer distances to get to transit, between a quarter- and a half-mile." Dittmar, H., and G. Ohland, eds. The New Transit Town: Best Practices in Transit-Oriented Development. 2004. Island Press. Washington, D.C. p. 120.
Survey of walking distance research (pdf) From Fairfax County, VA Planning Board.