We report a pressure sensor based on a suspended gate carbon nanotube field-effect transistor using a diaphragm measuring $3~\mu \text{m}$ in radius. The significant diaphragm size reduction is achieved by using high-quality low-stress atomic layer deposited aluminum oxide. The measurements show a reversible pressure dependence of the transistor current. A normalized sensitivity in the order of 10%/bar is determined, which is comparable with the state of the art despite the significantly reduced footprint of the active sensor elements. The devices operate at only 30 nW due to the low-power carbon nanotube transistor. [2015-0276]