Membership in religious institutions in the United States declined last year by more than half a million members, according to the just-published 1982 Yearbook of American and Canadian Churches.

The annual compilation of statistics, produced by the National Council of Churches, indicates that mainline Protestant churches suffered the largest losses, with Roman Catholics, Jews and conservative evangelicals all registering gains.

The volume indicates that 115,590,825 Americans, or 58.7 percent of the population, are counted by some church or synagogue as a member.

The 290-page Yearbook includes statistics and other basic information on 218 different religions in this country, 82 in Canada and a directory of national and international institutions, organizations and publications related to organized religion. It also provides reports on trends among the churches.

In one such report, on the effects of inflation on the collection plate, Yearbook editor Constant H. Jacquet Jr. found that churches have fared relatively well over the last two decades. In terms of 1967 dollars, Jacquet reported, per capita giving increased from $77.01 in 1961 to $86.47 in 1980.

In another report, two sociologists of religion, Dr. William McKinney of the United Church of Christ in New York and Dr. Wade Clark Roof of the University of Amherst, analyzed data gathered by several research organizations to study 26 American religious groups.

Among their findings:

* Women are a majority in all groups studied except the Reformed Church and some evangelical and fundamentalist churches; women make up over 60 percent of the membership of Christian Scientist, Episcopal, Jehovah's Witnesses, Unitarian, Mormon, black southern Baptist, and Adventist churches.

* Members of mainline Protestant churches tend to be older. Members aged 55 or over make up 45 percent of the Disciples of Christ; 43 percent of Methodists; 42 percent of Northern Presbyterians; and 40 percent of the United Church of Christ. The figure is 56 percent for Christian Scientists. Members over 55 made up fewer than 40 percent of all the conservative Protestant denominations studied.

* In liberal and moderate Protestant denominations, where the sharpest membership declines have occured, the birth rate among women in their child-bearing years is below the population replacement level of 2.1 children. These are also the denominations with fewer members under 45, leading McKinney and Roof to suggest that "member fertility" is a "contributing factor to the contrasting growth patterns" of liberal and conservative Protestantism.

* Highest incidence of divorce was found in the three black groups studied: black Methodists and black Baptists in the north and south. Mormons, Catholics and members of the United Church of Christ and Disciples of Christ had the lowest divorce rate. The highest percentage of persons who have never married -- 19 -- was found among black Methodists and black northern Baptists; the lowest percentage -- one -- among Episcopalians.

* Unitarian-Universalists, Jews and Episcopalians, in that order, have the highest educational levels. Northern Presbyterians edge out Episcopalians in the percentage of families with incomes over $20,000. The three black Protestant groups have the most families with incomes under $10,000.

Publication of the Yearbook this year coincided with the 1982 Official Catholic Directory, which reports that the Catholic Church, the nation's largest single denominiation, grew by more than 750,000 members last year.

The nation's 51,207,579 Roman Catholics made up 22.17 percent of the total population.

After more than a decade of decline, Catholic school enrollment increased by 32,744 students last year. But the bad news for the church was the net loss of 313 priests.

Even more alarming for the church was the continuing decline in candidates for the priesthood.

The 11,645 seminarians today are less than a quarter of the number 10 years ago.