A nuclear family, elementary family or conjugal family is a family group consisting of two parents and their children (one or more). It is in contrast to a single-parent family, to the larger extended family, and to a family with more than two parents. Nuclear families typically center on a married couple; the nuclear family may have any number of children. There are differences in definition among observers; some definitions allow only biological children that are full-blood siblings, but others allow for a stepparent and any mix of dependent children including stepchildren and adopted children.
Family structures of a married couple and their children were present in Western Europe and New England in the 17th century, influenced by church and theocratic governments. With the emergence of proto-industrialization and early capitalism, the nuclear family became a financially viable social unit. The term nuclear family first appeared in the early twentieth century. Alternative definitions have evolved to include family units headed by same-sex parents and perhaps additional adult relatives who take on a cohabiting parental role; in the latter case, it also receives the name of conjugal family.
The concept that narrowly defines a nuclear family is; central to stability in modern society that has been promoted by familialists who are social conservatives in the United States, and has been challenged as historically and sociologically inadequate to describe the complexity of actual family relations. In "Freudien Theories of Identification and Their Derivatives" he states "Very little is known about the extent variation in the behavior of fathers and mothers towards sons and daughters, and even less about the possible effects on such differential treatment." Little is known about how parental behavior and identification processes work, and how children interpret sex role learning. In his theory he uses "identification" with the father in the sense that the son will follow the sex role provided by his father and then for the father to be able identify the difference of the "cross sex" parent for his daughter.
Historians Alan Macfarlane and Peter Laslett postulated that nuclear families have been a primary arrangement in England since the 13th century . This primary arrangement was different than the normal arrangements in Southern Europe, in parts of Asia, and the Middle East where it was common for young adults to remain in or marry into the family home. In England multi-generational households were uncommon because young adults would save enough money to move out, into their own household once they married. Sociologist Brigitte Berger argued, "the young nuclear family had to be flexible and mobile as it searched for opportunity and property. Forced to rely on their own ingenuity, its members also needed to plan for the future and develop bourgeois habits of work and saving." Berge also mentions that this could be one of the reasons why the Industrial Revolution began in England and other Northwest European countries. However, the historicity of the nuclear family in England has been challenged by Cord Oestmann. 
As a fertility factor, single nuclear family households generally have a higher number of children than co-operative living arrangements according to studies from both the Western world and India.
There have been studies done that shows a difference in the number of children wanted per household according to where they live. Families that live in rural areas wanted to have more kids than families in urban areas. A study done in Japan between October 2011 and February 2012 further researched the effect of area of residence on mean desired number of children. Researchers of the study came to the conclusion that the women living in rural areas with larger families were more likely to want more children, compared to women that lived in urban areas in Japan.
In its most common usage, the term nuclear family refers to a household consisting of a father, a mother and their children all in one household dwelling. George Murdock, an observer of families, offered an early description:
The family is a social group characterized by common residence, economic cooperation and reproduction. It contains adults of both sexes, at least two of whom maintain a socially approved sexual relationship, and one or more children, own or adopted, of the sexually cohabiting adults.
Many individuals are part of two nuclear families in their lives: the family of origin in which they are offspring, and the family of procreation in which they are a parent.
While the phrase dates approximately from the Atomic Age, the term "nuclear" is not used here in the context of nuclear warfare or nuclear power, but instead originates in the same root as nuclear fission, the word "nuclear" originating in the Lating nucleus, itself originating in the Latin nux, meaning "nut", i.e. the core of something – thus, the nuclear family refers to all members of the family being part of the same core rather than directly to atomic weapons.
An extended family group consists of non-nuclear (or "non-immediate") family members considered together with nuclear (or "immediate") family members.
In 2005, information from the United States Census Bureau showed that 70% of children in the US live in traditional two-parent families, with 66% of those living with parents who were married, and 60% living with their biological parents. The information also explained that "the figures suggest that the tumultuous shifts in family structure since the late 1960s have leveled off since 1990".
When considered separately from couples without children, single-parent families, and unmarried couples with children, the United States traditional nuclear families appear to constitute a minority of households – with a rising prevalence of other family arrangements. In 2000, nuclear families with the original biological parents constituted roughly 24.10% of American households, compared with 40.30% in 1970. Roughly two-thirds of all children in the United States will spend at least some time in a single-parent household. According to some sociologists, "[The nuclear family] no longer seems adequate to cover the wide diversity of household arrangements we see today." (Edwards 1991; Stacey 1996). A new term has been introduced, postmodern family, intended to describe the great variability in family forms, including single-parent families and couples without children." Traditional nuclear family households are now less common compared to household with couples without children, single-parent families, and unmarried couples with children.
In the UK, the number of nuclear families fell from 39.0% of all households in 1968 to 28.0% in 1992. The decrease accompanied an equivalent increase in the number of single-parent households and in the number of adults living alone.
According to some sociologists, "[The nuclear family] no longer seems adequate to cover the wide diversity of household arrangements we see today." (Edwards 1991; Stacey 1996). A new term has been introduced, postmodern family, intended to describe the great variability in family forms, including single-parent families and couples without children."
Professor Wolfgang Haak of Adelaide University, detects traces of the nuclear family in prehistoric Central Europe. A 2005 archeological dig in Elau in Germany, analyzed by Haak, revealed genetic evidence suggesting that the 13 individuals found in a grave were closely related. Haak said, "By establishing the genetic links between the two adults and two children buried together in one grave, we have established the presence of the classic nuclear family in a prehistoric context in Central Europe.... Their unity in death suggest[s] a unity in life." This paper does not regard the nuclear family as "natural" or as the only model for human family life. "This does not establish the elemental family to be a universal model or the most ancient institution of human communities. For example, polygamous unions are prevalent in ethnographic data and models of household communities have apparently been involving a high degree of complexity from their origins." In this study evidence suggests that the nuclear family was embedded with an extended family. The remains of three children (probably siblings based on DNA evidence) were found buried with a woman who was not their mother but may have been an "aunt or a step-mother".
For social conservatism in the United States and Canada, the idea that the nuclear family is traditional is an important aspect, where family is seen as the primary unit of society. These movements oppose alternative family forms and social institutions that are seen by them to undermine parental authority.