The promising news that not just one but two coronavirus vaccines were more than 90 percent effective in early results has buoyed hopes that an end to the pandemic is in sight.

But even if the vaccines are authorized soon by federal regulators — the companies developing them have said they expect to apply soon — only a sliver of the American public will be able to get one by the end of the year. The two companies, Pfizer and Moderna, have estimated they will have 45 million doses, or enough to vaccinate 22.5 million Americans, by January.