converse: Breaking point formula by Converse

Description Usage Arguments Details Value Author(s) References See Also Examples


Calculating the breaking point between two cities or retail locations


converse(P_a, P_b, D_ab)



a single numeric value of attractivity/population size of location/city a


a single numeric value of attractivity/population size of location/city b


a single numeric value of the transport costs (e.g. distance) between a and b


The breaking point formula by Converse (1949) is a modification of the law of retail gravitation by Reilly (1929, 1931) (see the functions reilly and reilly.lambda). The aim of the calculation is to determine the boundaries of the market areas between two locations/cities in consideration of their attractivity/population size and the transport costs (e.g. distance) between them. The models by Reilly and Converse are simple spatial interaction models and are considered as deterministic market area models due to their exact allocation of demand origins to locations. A probabilistic approach including a theoretical framework was developed by Huff (1962) (see the function huff).


a list with two values (B_a: distance from location a to breaking point, B_b: distance from location b to breaking point)


Thomas Wieland


Berman, B. R./Evans, J. R. (2012): “Retail Management: A Strategic Approach”. 12th edition. Bosten : Pearson.

Converse, P. D. (1949): “New Laws of Retail Gravitation”. In: Journal of Marketing, 14, 3, p. 379-384.

Huff, D. L. (1962): “Determination of Intra-Urban Retail Trade Areas”. Los Angeles : University of California.

Levy, M./Weitz, B. A. (2012): “Retailing management”. 8th edition. New York : McGraw-Hill Irwin.

Loeffler, G. (1998): “Market areas - a methodological reflection on their boundaries”. In: GeoJournal, 45, 4, p. 265-272

Reilly, W. J. (1929): “Methods for the Study of Retail Relationships”. Studies in Marketing, 4. Austin : Bureau of Business Research, The University of Texas.

Reilly, W. J. (1931): “The Law of Retail Gravitation”. New York.

See Also

huff, reilly


# Example from Huff (1962):
converse (400000, 200000, 80)
# two cities (population 400.000 and 200.000 with a distance separating them of 80 miles)

Example output

[1] 46.86292

[1] 33.13708

REAT documentation built on Nov. 21, 2019, 5:08 p.m.