The instrument used to measure air pressure is called a barometer.

What a barometer is

A barometer is a scientific device that measures atmospheric (air) pressure, usually in units like millibars (mb), hectopascals (hPa), or millimeters/inches of mercury (mmHg or inHg). Meteorologists use it to track weather patterns, because falling or rising pressure often signals storms or clearer conditions.

Common types of barometers

  • Mercury barometer : Uses a column of mercury in a glass tube; very accurate but fragile and less common today.
  • Aneroid barometer : Uses a sealed metal cell that bends with pressure changes, linked to a dial; widely used in homes and weather stations.
  • Digital barometers / pressure sensors : Electronic versions that give fast, precise readings and are common in smartphones, weather stations, and aviation equipment.

In short, whenever you see a number for “air pressure” in weather reports or on a home device, it was almost certainly measured by some kind of barometer.

TL;DR
The instrument used to measure air pressure is a barometer ; typical types are mercury, aneroid, and digital barometers.

Information gathered from public forums or data available on the internet and portrayed here.