Rank Size Rule Calculator

This calculator uses the Rank Size Rule to determine the ideal number of facilities needed based on population distribution. The rule states that the population served by the nth facility should be approximately n² times the population served by the first facility.

Input Parameters

Calculation Results

Rank Size Rule Results

Enter the population and number of facilities to see results.

Calculation Formula

Pn = n² × P1

Where:
Pn = Population served by the nth facility
n = Facility rank (1, 2, 3, ...)
P1 = Population served by the first facility (P1 = Total Population / Number of Facilities)

Rank Size Rule Calculator Usage Guide

Learn how to use the Rank Size Rule Calculator to optimize facility distribution based on population needs.

How to Use This Calculator

  1. Enter the total population in the area you're analyzing.
  2. Specify the desired number of facilities to be distributed across the population.
  3. Click the "Calculate" button to see the recommended population distribution for each facility.
  4. Use the results to plan facility locations and resource allocation.

Understanding the Rank Size Rule

The Rank Size Rule is a mathematical formula used in planning to determine the ideal size or capacity of facilities based on population distribution. The basic principle is that the population served by each facility should increase with the square of its rank in the system.

For example, if you're planning 3 facilities for a population of 1000:

  • The first facility would serve approximately 333 people (1000 / 3)
  • The second facility would serve approximately 1333 people (4 × 333)
  • The third facility would serve approximately 4000 people (9 × 333)

This rule helps ensure that facilities are distributed in a way that maintains balance and efficiency across the system.

When to Use This Calculator

This calculator is particularly useful in:

  • Public transportation planning
  • School district planning
  • Hospital network design
  • Library system development
  • Community facility planning