What are township range and sections on a map and how do I figure out the quarter section of the section?

Answer

Quarter Section: One quarter of the 640 acre Section, each Quarter Section being 160 acres, named Northeast (NE/4), Southeast (SE/4), Northwest (NW/4), and Southwest Quarters (SW/4).

Exception I: Quarter Sections designated as Lots may (and usually do) vary in acreage. Due to the curvature of the earth, some Townships contain Sections on the North and/or West sides in which the exterior (perimeter) of the Quarter of a Quarter Section - e.g. N/2 (North half) NE/4 NE/4 may be designated as a Lot. If so each half along the perimeter of th Quarter of a Quarter along that side of the Section would be numbered as a Lot. E.g. N/2 NE/4 NE/4 = Lot 1, N/2 NW/4 NE/4 = Lot 2, N/2 NE/4 NW/4 = Lot 3, etc. Therefore that Quarter of a Quarter Section will not contain 40 square acres, the Quarter Section will not contain 160 square acres and the Section will not contain 640 square acres.

Exception II: A river may change course and "take" land formerly surveyed as being part of a given Quarter Section, thus changing the areage.

Section: Basic unit of the system, a square tract one mile from East to West and one mile from North to South containing 640 acres.

Township: 36 Sections arranged in a 6 by 6 array, measuring 6 miles by 6 miles. Sections are numbered beginning with the Northeast-most Section, proceeding West to 6, then South along the West edge of the Township and back to the East for Sections 7 - 12, etc.

Range: Assigned to a Township by measuring East or West of a Principal Meridian

Range Lines

North to South lines which mark Township boundaries

Township Lines: East to west lines which mark Township boundaries

Principal Meridian: Reference or beginning point for measuring East or West ranges.