If every public high school in Virginia offered college admission tests free, the supply of graduating seniors who could compete for entry to major universities within the state would grow significantly, according to a study released Tuesday.

The pool of prospects for the highly selective University of Virginia and College of William & Mary would expand nearly 20 percent, the study from U-Va. researchers found, and as much as 40 percent for broader-access public universities. The boost would be especially notable, the study found, for students from poor families who otherwise might not think about signing up to take the SAT or ACT.

But universal testing has been slow to catch on in Virginia even though many states and school systems elsewhere pay to provide one of the two major admission tests during the school day.

Public schools in the District and in Montgomery and Prince George’s counties in Maryland offered the SAT in the last school year and plan to do so in the coming year. The College Board, which owns the SAT, has contracts to provide the test statewide in Connecticut, Illinois, Michigan, West Virginia and several other states. The ACT has similar arrangements with more than a dozen states, including Alabama and Wyoming. Those contracts can bring major revenue to testing agencies.

Virginia state officials say 47 public high schools offered the SAT free in the last school year. Several were in Richmond and Henrico County. The only one in Northern Virginia was T.C. Williams High in Alexandria. The Fairfax County school system, Virginia’s largest, said it is considering the idea for the 2020-2021 school year.

At T.C. Williams, 584 students took the SAT on a March school day. The average score was 1032 and the highest was 1520, out of a maximum 1600. Peter Balas, the school’s principal, said he heard from some students who were surprised at how well they did.

“It opens doors,” Balas said. “It includes kids who maybe weren’t thinking about college before.”

The testing is free for students, but not the school system. Alexandria officials said the system paid the College Board about $44,000 in the last school year for the SAT and a companion preliminary exam known as the PSAT/NMSQT. It was the second year T.C. Williams has offered the SAT free. More than 60 percent of Alexandria students come from households with enough financial need to qualify free or reduced-price meals.

The study released Tuesday analyzed data on the academic performance of students in the 2014 graduating class who didn’t take the SAT. Those “non-takers,” it turns out, included many with high potential who might have been overlooked because their names and addresses weren’t on test-score lists.

“If you can’t find them, it’s hard to recruit them,” said Sarah Turner, a professor of economics and education at U-Va. She co-authored the study, published in a peer-reviewed journal by the American Educational Research Association, with Emily E. Cook, a PhD candidate in economics at U-Va.

Cook and Turner used state test scores and demographic data to predict what would have happened if non-takers had completed the SAT. They focused on the SAT because historically, it has had a much larger share of the admission-testing market in Virginia than the ACT.

About 32,900 students in the class, or about 44 percent of the total, didn’t take the SAT. Of those, the researchers estimated that about 8,000 would have scored at least 1000 on the exam’s math and reading sections. They estimated that about 1,800 would have scored 1200 or better — marks that might have put them in contention that year, or nearly so, for schools such as U-Va. or William & Mary. Test scores are one of many factors those universities use, along with grades, course selection and extracurricular activities, to select an entering class.

Not all universities require the SAT or ACT. A growing number are test-optional, meaning applicants can choose whether to submit scores. Enrollment chiefs at these schools say grades and other elements of an application are sufficient to predict academic potential.

Among the latest to drop testing requirements are the private University of Rochester in New York and Marquette University in Wisconsin, for classes entering in fall 2020. Last year, the private University of Chicago also went test-optional. In Virginia, public James Madison University is test-optional. Old Dominion and Virginia Commonwealth universities, also public, allow applicants with a minimum grade-point average to choose not to submit test scores.

Virginia’s secretary of education, Atif Qarni, declined through an aide to comment on universal admission testing. The state superintendent of public instruction, James F. Lane, said in a statement that providing all students access to SAT and ACT testing “would be beneficial in providing students with equitable academic opportunities.” He said public funding and philanthropy “could help ensure students have equitable access and provide the support students need to be successful on the test.”

Proposals to fund a statewide program have been discussed in the state legislature but not enacted.

Turner said offering admission testing in all schools would require trade-offs.

“If you make everybody take the test, you are going to increase costs, obviously,” she said. Some burden would also fall, she said, “on students who may have no interest in college” and do not want to take a three-hour test that has no meaning for them.

In Maryland, educators say the payoff is worth it. Scott Murphy, director of secondary curriculum and districtwide programs for Montgomery schools, said about 8,000 juniors took the SAT during school days in the last school year. The annual cost is about $450,000. “We have found this effort to be an important step to removing barriers associated with college entrance examinations and ensures access for all students,” Murphy said.

Prince George’s school officials said the testing program is a hit with the community.

“Educational equity,” said county schools chief Monica Goldson, means “having adequate and appropriate access for each student to achieve their highest potential. In providing free SAT testing during the school day, we expand the pathway to higher education and help students to see opportunities that they may not have otherwise considered.”