### Fractional Sections and the Relationship of Chains to Acres

```GLOSurveying
Fractional Sections and the
Relationship of Chains to Acres
ne of the interesting aspects of the U.S. Public
Land Survey System (USPLSS) is the unique
relationship between chains and acres. For
those who work with the USPLSS, and the
records of same, often the Township Plats
contain acreage and fractional part distances
that are either difficult to read, partially missing or, in some
instances, incorrect.
There are three convenient rules available to apply in
working with these matters when one understands the unique
relationship between chains and acres. Before discussing these
rules it might be helpful to review this relationship through
deductive definitions, as follows:
■1 Chain = 66 feet, by definition
■1 Statute Mile = 5,280 feet, by definition
■1 Acre = 43,560 square feet, definition
Thus, 5,280/66 = 80, and 80 chains = 1 Statute Mile
One theoretical Section of Land is one mile on a side, or 80
chains, or 5,280 feet
5,280 X 5,280 = 27,878,400/43,560 = 640 acres
Or, 80 Chains X 80 Chains = 6,400/10 = 640 acres
Thus, Area (in acres) = Width (in chains) X Length (in
chains)/ 10
For example, in a theoretical Quarter-Quarter Section, being
20 chains by 20 chains, the product is 400. Divided by 10, the
result is 40 acres.
Given the above definitions and relationships, and working
with lengths of sides in chains, and areas in acres, one can
derive the following three rules:
By multiplying the average width (in chains) of a fractional
lot or aliquot part by the average length (in chains), and
dividing by 10, one can derive the area in acres.
The area of an aliquot part (in acres), minus an adjoining side
(in chains), will equal the length of the opposite side (in chains).
The area of a lot (in acres), added to the area (in acres)
of an adjoining lot, divided by 4, will equal the distance (in
chains) of the common side. This rule does not work, however,
when applied to aliquot parts of differing size (e.g., a 40 ac.
and an adjoining 80 ac. part), but is valid where convergence
of meridians is involved in fractional lots adjoining the west
boundary of a township. And, the area in acres of each lot
in the west tier is found by adding the lengths in chains of its
north and south boundaries, or for the north tier of lots (except
Lot 4 of Section 6), by adding the lengths in chains of the west
and east boundaries.
It should be noted that minor differences will sometimes occur
using these rules. These differences should be averaged to resolve
the discrepancies. On can also check the results from these rules
by proportioning, for example, the exterior dimension shown on a
tier of fractional lots across the Section’s north or west side, to the
opposite exterior, using the difference divided by 4, and distributing across to derive the three interior lot dimensions of the tier of
four lots. The three rules can also be applied to determine if, and
to locate where, an error has occurred on the Township Plat.
Above is a diagram from the Manual of Surveying