# Extensive Definition

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.

## Description

A nomogram typically has three scales: two scales represent known values and one scale is the scale where the result is read off. The known scales are placed on the outside; i.e. the result scale is in the center. Each known value of the calculation is marked on the outer scales and a line is drawn between each mark. Where the line and the inside scale intersects is the result. The scale marks include 'tick marks' to indicate exact number locations, and labeled reference values. These scales may be linear, logarithmic or have some more complex relationship. Straight scales are useful for relatively simple calculations, but for more complex calculations, simple or elaborate curved scales may need to be used.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.

## Examples

- The Smith chart (see figure, right), used in electronics and systems analysis
- Nonlinearly ruled graph paper (probability rule, semi-log rule or log-log rule) all intended to represent various non-linear functions as straight lines on a graph.
- Thermodynamic diagrams and tephigrams, used to plot the vertical structure of the atmosphere and perform calculations on its stability and humidity content.

### Parallel-resistance/thin-lens nomogram

The nomogram below performs the computation- \frac

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 green line demonstrates
that parallel resistors of 56 and 33 ohms have a combined resistance of
about 21 ohms. It also demonstrates that an object at a
distance of 56 cm from a lens whose
focal
length is 21 cm forms a real image at
a distance of about 33 cm.

### Chi-squared test computation nomogram

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

- \frac

The blue line demonstrates the computation
of

- (9 − 5)2/ 5 = 3.2

The red line demonstrates the computation
of

- (81 − 70)2 / 70 = 1.7

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.

## External links

- Links to nomographs available on the web.
- Nomogram from Wolfram Research
- Atmospheric nomogram (pdf) from the Department of Meteorology, University of Reading.
- PyNomo package to make nomograms with Python.
- The Art of Nomography describes the design of nomograms using geometry, determinants, and transformations.
- Nomograms for Wargames but also of general interest.
- Javascript Applet for constructing simple nomograms.
- Sigma-Aldrich Pressure-Temperature Nomograph Quickly and easily estimate boiling points at various pressures.

nomography in Czech: Nomogram

nomography in Danish: Nomogram

nomography in German: Nomogramm

nomography in Spanish: Nomograma

nomography in Japanese: ノモグラム

nomography in Polish: Nomogram

nomography in Portuguese: Nomograma

nomography in Slovak: Nomogram

nomography in Swedish: Nomogram

nomography in Ukrainian:
Номограма