'half a jar' is a grammatically correct and usable phrase in written English.
You can use it to describe an amount of something that is less than the full amount contained in the jar. For example, "I only had half a jar of jam to use for my toast this morning."
Becher's recipe for imitation lemon-meringue consists of: 2 handfuls of shredded white paper, Half a jar of library paste, yellow Easter egg dye.
Popcorn: mincemeat popcorn (mix half a jar of mincemeat into a bowl of popped corn, spread out on a tray and bake until dry – about 10 minutes at 180C/350F/gas mark 4).
I decided to use ingredients that we had on hand, ingredients that Tom likes: bow tie pasta, onions, carrot, half a jar of water packed artichokes and a third of a jar of capers.
You will need jam too, not much, less than half a jar of apricot.
And then, never having felt less festive, I found half a jar of mincemeat and remembered the Strict Baptist tart.
The British now eat just half a jar of honey each a year, while downing their weight (53kg) in refined sugar.
All the team have is a kettle and half a jam jar of sugar to confront a death toll anthropologists fear could wipe out the Tiwis within two generations.
Its origins lie in a study by a Nobel laureate, Otto Meyerhof, who in the early years of the 20th century cut a frog in half and put its bottom half in a jar.
The 50-50 way is one that most use; meaning: When you get money, use only half of it, and stash the other half in a jar or something.
The other two models, Jar and Eclipse, look similarly weird, and feature half of a jar or an eclipse.
One day, I woke up after a night of drinking and there was half a pickle jar left.
