If you have two identical grocery stores to choose from, one five minutes away and one 40 minutes away, you will almost always choose the closer one. This everyday decision illustrates a key concept in geography.
Distance decay describes how interactions between two places weaken as the space between them grows. Though this idea may sound obvious, its applications span urban planning, retail strategy, transportation modeling, and tourism analysis. Geographer Waldo Tobler formalized this concept in 1970 as geography’s first law: Everything is related to everything else, but near things are more related than distant things.
This idea helps explain how businesses perform, why people choose certain commutes, and how neighborhoods are visited. For anyone making decisions about locations, distance decay is a helpful way to understand how people move and interact in space.
Table of Contents
The gravity model remains the most common way to model distance decay. Borrowed from physics, it treats human interaction between two places as proportional to their populations and inversely proportional to the square of the distance between them. Larger populations generate more interaction. A greater distance reduces it.
This model has been applied for decades to migration, trade, commuting, and retail behavior. Its simplicity allows analysts to estimate trips, calls, or transactions between places using only population and distance.
There is a debate about how best to show distance in the decay formula. The original version uses an inverse power law, meaning interaction drops steadily as distance grows. In this model, a place’s influence weakens with distance but never completely disappears.
A study of Chinese cities examined this closely. Researchers found that the power-law decay best fits large, complex regions: a city’s influence stretches far, weakening but still noticeable even at a distance.
Another approach is using exponential decay. In this method, influence drops off rapidly beyond a certain distance and eventually disappears. This approach often works well in situations where physical limits are essential, such as walking or short shopping trips.
Choosing between these models is vital in real life. For example, a business will set different market boundaries depending on which decay formula it uses.
David Huff created his probability model in 1963, and it’s now a common tool for choosing store locations and analyzing trade areas. The Huff model estimates how likely someone is to visit a store based on three factors: how far away it is, how attractive it is, and how far and attractive other stores are.
Attractiveness typically refers to store size, measured in square footage, though analysts sometimes include other variables like product selection or brand reputation. The model assumes that larger stores attract customers from farther away, while smaller stores serve a more local clientele.
In the Huff model, distance is not measured as a straight line. People do not perceive a place as twice as far as they do as simply twice as difficult to reach. Instead, the barrier created by distance increases more sharply as the distance grows. For example, a store two miles away feels significantly farther than one just a mile away.
This friction varies by trip purpose. The model uses a distance decay parameter, represented by the Greek letter beta, to account for these differences. Grocery shopping has a large beta value, meaning people will travel only short distances. The weekly trip for bread and milk does not justify a long drive. Furniture shopping has a lower beta because people are willing to travel farther for infrequent, high-value purchases.
A 2024 study in the Journal of Transport Geography examined the factors that shape distance-decay patterns. Using data from an extensive national travel survey, the researchers tested which variables best predicted the decline in travel with distance.
They found four main factors: how people travel, why they travel, whether places are urban or rural, and the travelers’ socioeconomic status.
Travel mode had the most substantial effect. Walking, driving, and public transit each produce distinct decay patterns. The study found that travel distance accounts for 42.28% of the explanatory power in predicting travel mode choice. For walking specifically, that figure rises to 63.24%. As distance increases, the physical effort required to walk increases, and the decay effect becomes more pronounced.
Why people travel also matters. Commuting to work looks different from going out for fun or shopping. People are willing to go farther for things they value, but not for everyday errands.
Where someone lives shapes their travel patterns. Crowded cities, suburbs, and rural areas each have distinct options, traffic patterns, and distributions, all of which matter.
Socioeconomic status also matters. Mobile phone data shows movement drops off faster with distance for vulnerable groups such as children, older adults, women, and people with lower incomes. In remote rural areas, people make fewer short trips, likely due to limited nearby services.
Mobile phone data and GPS tracking have changed how researchers study distance decay. These tools let them see real movement patterns at a large scale, rather than relying on surveys or theories.
A 2023 study in Bratislava, Slovakia, looked at mobile phone data from almost a million people over two weeks. For trips within the city, a specific mathematical formula best describes how distance makes travel harder. But in some city areas, there was little or no decay, suggesting that local conditions and city layout can affect how people move.
Researchers have also used GPS tracking in logistics. In the Guangdong-Hong Kong-Macau Greater Bay Area, a study looked at over 180 million GPS points from trucks. They created a method to measure truck flows and travel distances between ports and inland sites. They found that the actual travel distance reduces the number of port connections and follows an exponential rather than a power-law pattern.
Studies using GPS found that 81% of people’s movements happen within one kilometer of home. The chance of moving farther drops off quickly. Age also matters. Older people tend to travel farther from home than younger people do.
Tourism researchers use distance decay to predict how many people visit certain places and to plan infrastructure. It explains why attractions near transport hubs attract more visitors than similar places farther away.
Studies of tourists near train stations show distance decay in action. Most visitors stay close to the station and spend more time there. This happens because walking takes effort, and the farther you go, the harder it gets, so fewer people walk long distances.
The Spatial Interaction model uses distance decay to predict travel patterns for transportation planning. However, it often struggles to account for local differences in small cities. Recent studies in Greater London have begun adding factors such as income, car ownership, and employment to improve the model’s accuracy.
Distance decay also matters for gas stations. Studies show people will drive up to a mile to save just three cents per liter. This shows that people care about minor price differences, but only if the station isn’t too far away.
Although distance decay seems less relevant as interactions move online, research shows otherwise. Studies find that website usage patterns display distance decay, with server location acting as a center and users clustering around it. Even virtually, distance decay shapes interaction patterns.
The meaning of distance has evolved from simple physical measurements to include relationships, technology, and virtual connections. Even as technology removes some barriers, distance continues to affect how people behave.
Knowing about distance decay helps businesses and planners choose better locations. Retailers can figure out their trade areas and spot markets that need more stores. Transportation agencies can plan routes, and urban planners can predict how new buildings will change movement patterns.
The Huff and gravity models provide methods for measuring distance decay, but their results depend on high-quality data. The distance decay values need to match local conditions and the type of activity. For example, a grocery store in a busy city faces different challenges than one in a suburb, and a logistics company in a large port area faces different distance-related challenges than a local delivery service.
Recent studies show that people who live far from shopping areas are more affected by distance than those who live close to shopping areas. This matters for choosing store locations. Opening a store in an area with few options could attract customers who are willing to travel farther than usual.
Distance decay also explains competition. If two businesses sell similar things at similar prices, most customers will pick the closer one. Knowing this helps with planning and market analysis.
Even with better transport and communication, distance still shapes what people do. Most people choose nearby options for daily tasks because they take less effort, time, and stress.
The first law of geography emphasizes the stronger relationship between nearby places compared to those farther apart. Distance decay quantifies this relationship and supports forecasting and planning for location, transportation, and marketing decisions.
Brad Crisp is the CEO at Maptive.com, based in Denver, CO and born in San Francisco, CA. He has extensive experience in Business Mapping, GIS, Data Visualization, Mapping Data Analytics and all forms of software development. His career includes Software Development and Venture Capital dating back to 1998 at businesses like Maptive, GlobalMojo (now Giving Assistant), KPG Ventures, Loopnet, NextCard, and Banking.
Call Us: 
