More than 70 million Americans who receive Social Security benefits can expect an inflation adjustment to their monthly checks next year that will be the largest in four decades.

Government inflation figures for August, released on Tuesday, point to a Social Security cost-of-living adjustment, known as the COLA, of 8.7 percent, according to an estimate by a nonpartisan group that lobbies for seniors. The Social Security Administration will announce the final figure on Oct. 13, after the release of September inflation data.

The 8.7 percent estimate by the group, the Senior Citizens League, is lower than the league’s prediction last month of 9.6 percent. The revision reflects the recent slight cooling of inflation to 8.3 percent. But if the league’s projection holds up, the COLA still would be the largest since 1981, when the inflation adjustment was 11.2 percent.

Rising Medicare premiums often take a significant bite out of COLAs; the premium for Part B (which covers outpatient services, like doctors’ visits) typically is deducted from Social Security benefits. Large increases in Part B can sharply reduce, or even eliminate, a COLA. But next year, most experts expect the standard Part B premium to rise very modestly, or even stay flat at the current $170.10 per month.

Medicare officials have signaled that any premium increase would be modest because of the unusual circumstances surrounding Aduhelm, the costly new drug for treating Alzheimer’s disease.

The Food and Drug Administration approved Aduhelm in June 2021 despite objections from the agency’s own scientific advisory panel. The drug initially was to carry an annual price tag of $56,000 per patient — a figure that the drug’s maker, Biogen, later reduced to $28,800.

Because Aduhelm is administered in outpatient settings, the cost would be borne by Part B, not Part D, the prescription drug plan. Medicare officials factored in anticipated Aduhelm costs when the agency announced a 14.5 percent increase in the standard monthly Medicare Part B premium for 2022, to $170.10.

Medicare ultimately decided to sharply limit coverage of Aduhelm — but let stand the large Part B increase, citing administrative hurdles to a midyear rebate to the tens of millions of Americans on Medicare. That means Part B enrollees are being overcharged roughly $10 per month this year, and Medicare has stated that the 2023 premium will be adjusted accordingly.

“Seniors are so accustomed to the Part B premium consuming so much of the COLA — I think they’re in for a pleasant surprise this year,” said Mary Johnson, a policy analyst for the league.

The 2023 COLA will give a significant boost to more than 70 million Americans — a group that includes 52.3 million people over age 65, along with a broader group that includes survivors of beneficiaries‌ and‌ people receiving disability benefits‌ and Supplemental Security Income, the program for very low-income people.

The COLA is calculated annually using a formula detailed in federal law. It uses one of the broadest government measures of inflation, known as the Consumer Price Index for Urban Wage Earners and Clerical Workers‌, or C.P.I.-W.‌

Social Security averages together the C.P.I.-W. figures during the third quarter of each year, and compares that with the previous year’s figure. For example, the 2023 COLA will be calculated by averaging together the C.P‌.I.-W. figures for the third quarter of 2022 and comparing that with the same averaged figures for 2021.