Most of us at the doctor’s office do as asked, helpfully extending an arm as a health care worker wraps it in a blood pressure cuff, uncrossing our legs as it begins to python-squeeze our bicep.

What most of us don’t know is that the reading will likely be off. Or why.

But now, Cambridge University researchers say they have solved the long-running mystery. Millions of Americans who should be diagnosed with high blood pressure slip through because the arm cuffs in medical offices often give readings nearly six points too low.

What sounds like a tiny gap has big consequences. It means that nearly one in three people with systolic [sis-tahl-ick] hypertension may go undiagnosed, leaving them at risk of heart attacks and stroke.

A blood pressure reading measures the force in your arteries as your heart pumps. It’s recorded as two numbers. The first is your systolic [siss-tahl-ick] pressure. The second is your diastolic [die-uh-stahl-ick] pressure.

A systolic reading of 140 or more usually indicates Stage 2 hypertension, and that can mean blood pressure-lowering medication.

The researchers say when a traditional cuff inflates around your arm, it briefly shuts the main artery, causing blood pressure in the vessels farther down your arm to plummet. The more that “downstream” pressure drops, the more the cuff underestimates your actual blood pressure.

High blood pressure is the world’s leading cause of premature death, but it rarely causes symptoms until things get serious. Delayed treatment can be bad news.

The good news is that simple fixes may work, like raising your arm briefly before the test begins. Someday, design changes to the cuffs may correct the issue altogether.