She was right. Her children are vaccinated, but she has tested each of them at least once after Covid-19 cases emerged in their schools. She’s also given tests away to friends: As cases have risen, test-center appointments are harder to come by, and rapid tests are selling out at stores.

Rapid Covid-19 antigen tests are a hot commodity this fall. You buy them at the store or online, twirl a swab around your nostrils and get a result in roughly 15 minutes. The rapid tests are far faster than a PCR test done at a medical office or drugstore, whose results can take days to process. PCR tests are still more sensitive at detecting the virus, however, and the tests work in different ways.

The BinaxNOW test, made by Abbott Laboratories, is the most widely available and commonly used over-the-counter rapid antigen test. Other rapid tests authorized by the U.S. Food and Drug Administration include the Ellume Covid-19 Home Test and the QuickVue test made by Quidel.

The tests are flying off drugstore shelves. Some schools and employers are using them in an effort to reduce transmission and quarantine times. And some people are requiring guests to use them before attending gatherings like weddings. President Biden’s new Covid-19 response plan aims to increase the accessibility and availability of the tests, which can cost $14 to $25 or more.

How reliable are the tests and when should we use them? Here’s what scientists say.

When you have symptoms

Rapid tests are at their most reliable when used in people who have symptoms, scientists say. In those cases, rapid tests hold up well against the PCR tests processed in labs, which are typically used to diagnose Covid-19 by doctors and generally take a day or more to process. Antigen rapid tests detect viral protein; the more sensitive PCR tests detect viral RNA.

So if you’re trying to determine whether your sneezing is due to allergies or Covid-19, or if your snotty 5-year-old has a cold or Covid, a rapid test is likely a good option.

“There have been studies that have shown that they compare very well—more than 80% of the time—to PCR tests when somebody is actively infectious,” says Gigi Gronvall, a senior scholar at the Johns Hopkins Center for Health Security who has led an effort to track the development and marketing of rapid tests.

If you are symptomatic and a rapid test is negative, monitor your symptoms, says Omai Garner, director of clinical microbiology for the UCLA health system. If they get worse, go get a PCR test. If there are no immediate appointments, take another rapid test.

Testing without symptoms

If you’ve been exposed to someone with Covid-19 but you don’t currently have any symptoms, rapid tests aren’t as reliable, scientists say.

However, rapid tests may be somewhat useful if you take them multiple times over several days, says Albert Ko, department chair of epidemiology of microbial diseases at the Yale School of Public Health. Screen yourself every two or three days, he suggests. “There’s a cumulative advantage of multiple testing.”

However, some doctors, including Dr. Garner, say if you are doing multiple rapid tests after an exposure you should still do a PCR test. If you have to wait five days for a PCR test, you can take a rapid test in between as a supplement, Dr. Garner says.

Doing the test correctly

The rapid tests you take at home work in the same way as a rapid test you would get at a medical office. The home tests may be less accurate because untrained people don’t always do the test correctly.

One study comparing the performance of rapid tests in a healthcare setting versus in a home found a small decrease in performance at home, attributed to laypeople making more mistakes, says Amy Karger, an associate professor in laboratory medicine and pathology at the University of Minnesota Medical School.

It is fairly straightforward if you read the instructions carefully, but not everybody does. You want to make sure you properly swab the inside of your nose on each side, doctors say.

“If you feel like you can’t get a good sample on yourself, ask someone else to help you to make sure you really get good coverage of that internal part of the nose on both sides,” Dr. Karger says. “If you don’t pick up enough of a sample, that could cause a false negative.”

Check the results at the time indicated in the instructions; reading results too early or late can lead to errors, Dr. Karger notes.

Testing before dinner parties, weddings and other gatherings

Scientists say that rapid home tests can be a useful tool—though not foolproof—in screening guests for events like weddings, indoor dinner parties or funerals. A rapid test won’t catch every case, but it will detect the most infectious people.

Alexandria Sage and her fiancé used rapid tests to screen guests before their wedding shower in Kansas City, Mo. “People came 15 minutes early, we handed them a test, they went back to the car, showed us the negative, and came inside,” says Ms. Sage, who is 30 and lives in Washington, D.C. The roughly 35 people attending all tested negative.

“My grandma, who is 91—this was the first time she was at an indoor event in like two years with all of our family together,” Ms. Sage said. “Our goal with this was to have everyone feel as comfortable as possible and to have some sense of normalcy.”

Such screening worries some doctors. Dr. Garner is concerned that rapid test results give asymptomatic people a false sense of security. “The goal is to be as sensitive as possible, you’re hoping to catch that person a day or two before having symptoms,” Dr. Garner says. “That’s a person you don’t want at your wedding.”