gauge

A device used to measure the amount, size, or pressure of something.

"Check the fuel gauge before starting the car."

To estimate or judge a situation, feeling, or reaction carefully.

"It was difficult to gauge his true intentions."

To measure the exact amount, size, or capacity of something precisely.

"Engineers will gauge the depth of the new tunnel."

A standard measure of thickness, diameter, or distance between rails.

"The railway line was built to a narrow gauge."