The most rigorous study to date of how much it costs to care for Americans with dementia found that the financial burden is at least as high as that of heart disease or cancer, and is probably higher. And both the costs and the number of people with dementia will more than double within 30 years, skyrocketing at a rate that rarely occurs with a chronic disease.

The research, led by an economist at the RAND Corporation, financed by the federal government, and published Wednesday in The New England Journal of Medicine, provides the most reliable basis yet for measuring the scale of the problem. Until now, the most-cited estimates of the condition’s cost and prevalence came from an advocacy group, the Alzheimer’s Association.

Although some figures from the new research are lower than the association’s projections, they are nonetheless staggering and carry new gravity because they come from an academic research effort. Behind the numbers is a sense that the country, facing the aging of the baby boom generation, is unprepared for the coming surge in the cost and cases of dementia.

“It’s going to swamp the system,” said Dr. Ronald C. Petersen, who is chairman of the advisory panel to the federal government’s recently created National Alzheimer’s Plan and was not involved in the RAND study.