A planimeter will give correct results for "any"
scale factor whatsoever, at least within the
tolerance imposed by the operator and a small
In practice, an operator will trace an area on a
plan with a known scale factor, and then multiply
the "raw" planimeter reading by a constant, Ca, to
get a corrected reading.
The constant Ca can be computed using an equation
given in the instructions that come with each
instrument. It is Ca = u*Sc^2 . "u" is the number of
square inches per planimeter count, unique for each
instrument and dependent on the arm length of that
instrument. It is provided with each instrument
shipped. Sc is the scale factor of the drawing to be
For example, suppose an Operator is using a
planimeter with its arm length set to medium length.
He or she should refer to the calibration record
that comes with the instrument and find that u is
0.017324 for a medium arm. The operator sees that
the scale factor for his or her drawing is 1:400,
meaning 1 unit = 400 units, where a unit can be an
inch, a foot, or whatever. For this example the
operator wants his answer to be in square feet so he
must convert his 1:400 scale to the number of inches
per foot. Since 1inch = 400 inches, it also equals
400 divided 12, or 33 1/3 feet. The hard part over,
he or she uses the equation and finds that Ca equals
0.017324*(33 1/3)^2 , or 19.249.
If the operator has a digital readout, he simply
keys in his scale factor of 19.249 and begins
measuring. His answer will be in terms of square
feet for each measurement. If the Operator has a
mechanical planimeter, he or she must manually
multiply each planimeter reading by
19.249 to get the number of square feet. If he or
she stores the 19.249 in a calculator memory, this
task becomes easier.
Some planimeters also give the value of u for metric
measurements, that is, u is the number of square
centimeters per planimeter count. In this case, the
operator might have to convert the scale factor to
give the number of centimeters per meter or whatever
before computing Ca.
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The EngineerSupply.com Product Team