eyeball
The round part of your eye that lets you see.
To eyeball something means to estimate or judge it roughly just by looking, without measuring precisely. When a chef eyeballs the amount of salt going into a pot, she's not measuring with a spoon but trusting her experience and visual judgment. When your dad eyeballs whether the couch will fit through the doorway, he's making a quick visual guess rather than getting out a tape measure.
The word captures that casual, confident way of sizing things up: “I'd eyeball that pile at about 50 rocks” or “Just eyeball how much water the plant needs.” It suggests you're close enough for the situation at hand, even if you're not mathematically exact.
The word can also mean to look at someone or something directly and intently. If someone's eyeballing you across the cafeteria, they're staring at you in a noticeable way. A security guard might eyeball suspicious activity in a store.
As a noun, your eyeball is the round part of your eye itself, the sphere that sits in your eye socket and lets you see. Doctors talk about eyeballs when discussing eye health, and the word appears in expressions like “up to your eyeballs in homework,” meaning you're completely overwhelmed with work, buried so deep that even your eyeballs are covered.