# Distance decay

Distance decay is a geographical term which describes the effect of distance on cultural or spatial interactions. The distance decay effect states that the interaction between two locales declines as the distance between them increases. Once the distance is outside of the two locales' activity space, their interactions begin to decrease.

With the advent of faster travel, distance has less effect than it did in the past, except where places previously well-connected by railroads, for example, have fallen off the beaten path. Advances in communications technology, such as phones, radio and television broadcasts, and internet, have further decreased the effects of distance.[1]

Distance decay is graphically represented by a curving line that swoops concavely downward as distance along the x-axis increases. Distance decay can be mathematically represented by the expression

$I = const. \times d^{-2}$ or $I \propto 1/d^2$,

where I is interaction and d is distance, among other forms, e.g. negative exponential,[2] i.e.

$I \propto e^{-d}$ .

Distance decay is also evident in town/city centres. It can refer to:

• the number of pedestrians getting further from the centre of the Central Business District(CBD),
• the street quality decreasing as distance from the centre increases as well,
• the quality of shops decreasing as distance from the centre also increases (though this may be an artifact of the definitions of 'quality' and 'centre')
• the height of buildings decreasing as distance from the centre increases
• the price of land decreasing as distance from the centre increases

It also weighs into the decision to migrate, leading many migrants to move less far than they originally contemplated.

## Related concepts

Related terms include "friction of distance," which describes the force that creates distance decay and Waldo R. Tobler's "First law of geography", an informal statement that "All things are related, but near things are more related than far things." "Loss of Strength Gradient" holds that the amount of a nation’s military power that could be brought to bear in any part of the world depends on geographic distance.