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Adair Township covers an area of 106.93 square miles (276.9 km2) and contains one incorporated settlement, Climax Springs. It contains nine cemeteries: Adkins, Barnumton, Cable Ridge, Clark, Dority, Granger, Parish, Whitaker and Woolery.
The streams of Bollinger Creek, Dry Branch, Fiery Fork, Jack Branch, Kolb Branch, Lick Creek, Morriss Creek, Pearson Branch, Rainy Creek, Rise Branch, Ritter Branch, Spring Valley Creek and West Pearson Branch run through this township, and it contains multiple smaller springs.
Adair Township contains the Moles Cave State Wildlife Area and Fiery Fork State Wildlife Area, which has canoe access to the Little Niangua River. It also contains the Climax Springs Lookout Tower.