A flag can be hung on a mast or a staff, but interestingly, a flag at half-mast or half-staff isn't hung exactly halfway down the pole.
The tradition of lowering the flag to show grieving and acknowledge death or tragedy likely began in 1612 when a British ship, Heart’s Ease, lost its captain at sea and returned to port with the flag lowered in his honor. Although we use the term “half mast,” it’s something of a misnomer because the flag is often lowered not halfway down the mast but by just the height of one flag. The story is that the Heart’s Ease sailors were making room for an invisible flag of death at the top, and the tradition has continued to this day.
To properly fly a flag at half-mast, tradition calls for the flag to actually be raised all the way to the top of the mast and then to be brought down to its lowered position.
We have two names for lowering the flag because flags can hang on staffs (on land) and on masts (on ships). Although many people aren’t aware of the difference, in general, a flag is flown at half-staff on land and half-mast on a ship.
And, of course, “half-mast” and “half-staff” can be used metaphorically. For example, describing people making a seductive gaze as lowering their eyelids to half-mast seems to be somewhat common in romance novels.
Finally, both "half-mast" and "half-staff" are hyphenated.
“So listen—one way to lower the flag to half-mast is just to lower the flag. There's another way though. You can also just raise the pole. You can raise the pole to like twice it's original height.” ― David Foster Wallace, Infinite Jest
“Indiana’s governor is directing that flags be lowered to half-staff across the state in honor of Rev. Billy Graham." FOX59
Mignon Fogarty is Grammar Girl and the founder of Quick and Dirty Tips. Check out her New York Times best-seller, “Grammar Girl’s Quick and Dirty Tips for Better Writing.”