Before a 22-day-old infant went to a doctor to be circumcised, his parents gave him a dose of acetaminophen to stave off the pain. But the parents misread the label. Instead of giving their baby 40 milligrams of acetaminophen like their doctor had recommended, these well-meaning parents gave him 800 milligrams, about half the bottle.

After the procedure, the doctor told the parents to give another dose of acetaminophen if the baby seemed uncomfortable. When the mother remarked that “it seemed like a lot of medicine,” the mistake was discovered.

Luckily, this little guy was fine. He was promptly treated with an antidote and suffered no lasting harm, doctors described in 2012 in the Canadian Medical Association Journal. Lots of other children aren’t so lucky. Accidental acetaminophen overdoses have been responsible for the deaths of 20 children between 2000 and 2009, according to this ProPublica story. (Some of these dangerous overdoses happened because Tylenol was sold in two different concentrations: Children’s and the more concentrated Infants’. Tylenol recently switched to just one concentration.)

Acetaminophen isn’t alone in confusing parents. About 40 percent of parents made mistakes when giving their children prescription medicine in a recent study. Researchers watched as parents re-created a medicine dose that they gave to their sick child after a visit to a New York City emergency room. About 40 percent of the parents got it wrong. That’s a lot of children who are getting too much or too little medicine. And these weren’t just little mistakes. Doses were off by more than 20 percent, researchers report in the August 2 Pediatrics.

The researchers don’t know whether any of these mistakes actually caused trouble. But theoretically, both overdosing and underdosing can be dangerous, says study coauthor H. Shonna Yin, a pediatrician at New York University School of Medicine and Bellevue Hospital Center. “Overdoses can lead to drug toxicity, while underdoses can lead to failure to appropriately treat a child’s illness,” she says.

Regrettably, it’s easy to blame parents for these mistakes. After all, how hard can it be to measure out medicine? As someone who spent years measuring small amounts of liquids and calculating exact concentrations in a lab, I can say that figuring out the right dose is actually much harder than it should be. When Baby V wakes up feverish in the middle of the night, milligrams, milliliters, kilograms and pounds all blur into a throbbing mess of urgent math agony.

But forget for a moment that we’re talking about worried, potentially sleep-deprived parents who might not be familiar with the medicine they’re dispensing. There are lots of other roadblocks to getting a dose right.

For starters, doctors, pharmacists, prescriptions and even the medicine bottle itself can describe doses in different units. Labels on nearly a third of medicine bottles in the new study contained units that differed from those in the prescription, for instance calling for a dose in teaspoons instead of milliliters, Yin and her team found.

Two of these common units invite a particularly pernicious problem: When a label (or a doctor or pharmacist) calls for a teaspoon or tablespoon of medicine, some parents reach for the kitchen drawer. Food spoons hold wildly different amounts of liquid, making it nearly impossible to get the dose right. About 17 percent of the parents in Yin’s study used a kitchen spoon rather than a syringe, dropper or dosing cup. That number might be low: One small study reported that over 70 percent of participants had used a kitchen spoon to dispense medicine.

Compared with parents who used milliliter units to measure a dose, parents who measured medicine in teaspoon or tablespoon units were twice as likely to make a dosing error, Yin and colleagues found. Switching to a standard system in which all liquid medicine is measured in milliliters would help prevent mistakes by doctors, pharmacists and parents, Yin says.

That sounds like a good idea to me. We ought to be doing everything we can to make it easier for parents to get the right dose of medicine into a sick kid.