gauge
To measure or judge the amount, size, or level of something.
Gauge (rhymes with “cage”) means to measure or estimate something, often when you can't get an exact number. When a teacher asks a tricky question to gauge how well the class understands a topic, she's trying to figure out whether students are ready to move forward or need more practice. A coach might gauge a player's energy level by watching how fast they run during warm-ups.
The word also refers to an instrument that measures something. A fuel gauge in a car shows how much gas is left in the tank. A rain gauge measures how much precipitation has fallen. Scientists use pressure gauges, temperature gauges, and many other types to measure all sorts of things.
Gauge can also mean the thickness, size, or capacity of something, especially in technical contexts. Railroad track gauge is the distance between the rails. Wire gauge describes how thick a piece of wire is (confusingly, higher gauge numbers mean thinner wire). Shotgun gauge indicates the diameter of the barrel.
When you're trying to gauge something like a friend's mood or a situation's difficulty, you're reading signs and clues to form a judgment, even without precise measurements.