A nomogram, nomograph, or abac is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a function. Like a slide rule, it is a graphical analog computation device; and, like the slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. Most nomograms are used in applications where an approximate answer is appropriate and useful. Otherwise, the nomogram may be used to check an answer obtained from an exact calculation method.
The slide rule is intended to be a general-purpose device. Nomograms are usually designed to perform a specific calculation, with tables of values effectively built in to the construction of the scales.
Usage is simple — a taut string or other straight edge is placed so as to contact the two known values on their lines. The required answer is read off another line. This allows calculation of one variable when the other two are known. Additional lines are sometimes added that are simple conversions of one of the other variables.
The nomogram below performs the computation
This nomogram is interesting because it performs a useful nonlinear calculation using only straight-line, equally-graduated scales.
A and B are entered on the horizontal and vertical scales, and the result is read from the diagonal scale. Being proportional to the harmonic mean of A and B, this formula has several applications. For example, it is the parallel-resistance formula in electronics, and the thin-lens equation in optics.
In the example below, the red line demonstrates that parallel resistors of 56 and 42 ohms have a combined resistance of 24 ohms. It also demonstrates that an object at a distance of 56 cm from a lens whose focal length is 24 cm forms a real image at a distance of 42 cm.
The nomogram below can be used to perform an approximate computation of some values needed when performing a familiar statistical test, Pearson's chi-square test. This nomogram demonstrates the use of curved scales with unevenly-spaced graduations.
The relevant expression is
The blue line demonstrates the computation of
The red line demonstrates the computation of
In performing the test, Yates' correction for continuity is often applied, and simply involves subtracting 0.5 from the observed values. A nomogram for performing the test with Yates' correction could be constructed simply by shifting each "observed" scale half a unit to the left, so that the 1.0, 2.0, 3.0, ... graduations are placed where the values 0.5, 1.5, 2.5, ... appear on the present chart.