Welcome to the Home Page of Church Growth Modelling

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Church Growth Modelling
What is Church Growth?
What is Church Growth Modelling?
The Models
Summary of Limited Enthusiasm Model
Details of Models
Limited Enthusiasm 
Births, Deaths & Reversion 
Effective Enthusiasts
Details of Results
Summary of Results
Short Term Revival
Long Term Growth
Long Term Decline
Growth via Renewal
Growth Through Spiritual Life
References & Bibliography 
Mathematics of Church Growth
Church Growth
System Dynamics
Sociology of Religion
Social Diffusion

Models for Download
Laws of Church Growth
Defence of Church Growth Modelling
Contemporary Revival-Like Movements
Church Growth Model Building Series


Church growth modelling is a research project that attempts to understand the growth and decline of the Christian Church using the techniques of mathematical sociology.

The models give valuable insights into the way the churches grow or decline at either a congregational, denominational, national or international level. They are particularly helpful in describing the dynamics of growth in times of revival.

This web site is aimed at church practitioners who wish to understand and enhance the growth of their churches, as well as academics looking for a quantitative understanding of the spread of religion.

Some important results are summarised below and on the Results Summary page.

A Blog contains short articles and commentaries on the project.

Moriah Chapel Loughor
Moriah Chapel, Loughor, near Swansea, South Wales.

One of the starting places of the 1904-5 revival in Wales and home church of revivalist Evan Roberts.

A revival is a sovereign work of God, giving new life to Christians. It leads to the conversion of many unbelievers and the transformation of communities.

Contact Details

John Hayward. Postal contact



Research details on the Social Dynamics web page.

Popular Documents

Recent Updates

What is Church Growth?

It is the discipline that seeks to analyse why Christian churches, at various levels of organisation, grow or decline. This includes both their spiritual growth as well as their numerical growth.

Church growth thinking can be divided into two strands:

The Church Strand, which is based with Christian denominations and exists to serve their needs. It is based on theological principles, organisational pragmatism, and ideas from the church growth movement.

The Social Science Strand whose focus is primarily academic research and has a basis in the sociology of religion.

Both strands use data gathering and statistical analysis to understand the nature of quantitative church growth.

What is Church Growth Modelling?

It is an attempt to understand the dynamics of church growth using mathematics and system dynamics methods.

Its aims are:

  • to produce theories of how churches grow, in the sense of why the numbers of people in churches change the way they do;  
  • to discover broad principles that describe the growth;  
  • to provide a theoretical framework that can both suggest and assess strategies of church growth;  
  • to help decide what sort of data should be gathered to best reflect a church's effectiveness;  

The project uses the techniques of mathematical sociology: differential equations and computer simulation. Significant use is made of the system dynamics methodology because of the quality of its model building processes and its accessibility to a non-technical audience. There is also input from statistics, sociology of religion, church history and christian belief.

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The Models

  1. Limited Enthusiasm Model. Based on social diffusion theories. Church grows through the activity of enthusiasts who are alone responsible for the recruitment/conversion of unbelievers into the church. Believers are only enthusiasts for a limited period after their conversion. Only new believers become enthusiasts. A basic model of revival growth. Model, Results. Application to revival.
    • Limited Enthusiasm with Births Deaths and Reversion. Model extended to include births, deaths, people leaving church and perhaps rejoining at a later date. Useful for analysing the long term survival of denominations and congregations. Model, Growth results. Decline results.
    • Renewal Model. As above but enthusiasts can also be made out of existing inactive believers. Models a range of renewal movements that start within the church. Shows that renewal is the key to seeing revival growth in the church. Model, Results.
    • Membership Model. Extension of the limited enthusiasm model to include the differences between church attendance and membership. Delays in joining and leaving a church cause attendance to run ahead of membership in a growing church, but run behind it in a declining church. This difference can be used as an indicator of future growth or decline, or of strictness in the church. Model, Results.
    • Effective Believers Model. An extension to the limited enthusiasm model where effectiveness depends on the production of spiritual activity. Explains the dynamics of how dying churches can be turned to living and growing ones through enthusiasts engaging in activities that bring spiritual life. Model started as a student project. Model, Results, blog post.
    • Church Planting. Extension of the limited enthusiasm model to include church planting strategies . Shows that growth in new churches can burn out due to a lack of enthusiasts rather than a lack of places to plant. The Migration model is a subset of this model. Model started as a student project. Migration Model, Migration Results.
  2. Congregational Models. Applied to the individual congregation only. Designed to assist church leaders. Based on ideas from business modelling.
    • Discipleship Model. A model of how the discipleship process progresses following conversion. This model was developed as part of the CICC Church Growth Cafe in Cardiff, UK. Model, Results.
    • Congregational Lifecycle Model. A model of a single congregation rather than a denomination or the whole church, linking the activity of church members and their ability to build "spiritual capital" as a resource to aid growth. Predicts the eventual slow decline of the church due to complacency and the need to spend more time on maintaining the resource and less on recruitment. Outlined in "Modelling Church Growth- Micro and Macro Models".
  3. Sociological Models. Based on theories in the sociology of religion.
    • Strictness Model. Explores the effect that the strictness of a church has on the growth of the church encapsulating Kelley's thesis that strict churches are strong and hence grow, but lenient ones are weaker and more likely to decline. See "A Dynamical Model of Strictness and its Effect on Church Growth 2002". Blog post Liberal and Conservative Churches Part 1.
    • Church and Society Model. An attempt to build current sociological theories such as secularisation, neo-secularisation and the new paradigm into a dynamic model and explore their relative effects. This acts as a useful macro-sociological comparison with the other micro-sociological models based on the activities of groups of people. Model is still in development.

The core models are published in peer reviewed journals and conferences in mathematics, sociology and system dynamics.

Models are built mainly using mathematics, or the System Dynamics methodology. This powerpoint presentation shows how System Dynamics is used to build a simple church growth model. (Also as a PDF).

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Summary of Limited Enthusiasm Model

Central Hypotheses

  • The faith is largely spread through enthusiasts, or "active" believers. These are active in recruitment distinguishing them from "inactive" believers who play little role in recruitment.   
  • Most conversion growth comes from contact between an enthusiast and an unbeliever. The numbers converted being proportional to the numbers of both.   
  • The enthusiastic phase of a believer only lasts a certain length of time, after which they become inactive.  

Key Results

  • There is a threshold over which large scale "revival-type" growth occurs. This depends on the number of unbelievers.  
  • The number of enthusiasts does not affect whether such substantial growth occurs. If there are smaller number enthusiasts the same growth occurs over as longer period.  
  • The threshold depends on the number of people converted per enthusiast.  Thus it is the "amount of enthusiasm" that governs the growth.
  • Growth will end because the church runs out of enthusiasts, not because the number of unbelievers runs out. As people are converted enthusiasts are less likely to meet unconverted people, leading to a failure to make sufficient enthusiasts.   
  • It is more beneficial for growth to increase the effectiveness of enthusiasts than to increase their numbers. A small number of effective evangelisers are better than a large number of less effective ones.  
  • When the population of a church is small compared to the surrounding unbelieving society it can be a long time before a revival among believers can see significant growth in the church. 
  • In summary it is the spiritual vitality of the enthusiasts that drives the growth of the church. More life gives more growth, provided that life is directed into contact with unbelievers. Read Acts 2:42-47 & 4:12-16 for a Biblical understanding of this principle.   
  • Go to Summary of Results for more.

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