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### 6.3 Other Nonlinear Units

Some other examples of nonlinear units are numerous different ring sizes and wire gauges, the grit sizes used for abrasives, the decibel scale, shoe size, scales for the density of sugar (e.g., baume). The standard data file also supplies units for computing the area of a circle and the volume of a sphere. See the standard units data file for more details. Wire gauges with multiple zeroes are signified using negative numbers where two zeroes is ‘-1’. Alternatively, you can use the synonyms ‘g00’, ‘g000’, and so on that are defined in the standard units data file.

```You have: wiregauge(11)
You want: inches
* 0.090742002
/ 11.020255

You have: brwiregauge(g00)
You want: inches
* 0.348
/ 2.8735632

You have: 1 mm
You want: wiregauge
18.201919

You have: grit_P(600)
You want: grit_ansicoated
342.76923
```

The last example shows the conversion from P graded sand paper, which is the European standard and may be marked “P600” on the back, to the USA standard.

You can compute the area of a circle using the nonlinear unit, ‘circlearea’. You can also do this using the circularinch or circleinch. The next example shows two ways to compute the area of a circle with a five inch radius and one way to compute the volume of a sphere with a radius of one meter.

```You have: circlearea(5 in)
You want: in2
* 78.539816
/ 0.012732395

You have: 10^2 circleinch
You want: in2
* 78.539816
/ 0.012732395

You have: spherevol(meter)
You want: ft3
* 147.92573
/ 0.0067601492
```

The inverse of a nonlinear conversion is indicated by prefixing a tilde (‘~’) to the nonlinear unit name:

```You have: ~wiregauge(0.090742002 inches)
You want:
Definition: 11
```

You can give a nonlinear unit definition without an argument or parentheses, and press Enter at the ‘You want: prompt to get the definition of a nonlinear unit; if the definition is not valid for all real numbers, the range of validity is also given. If the definition requires specific units this information is also displayed:

```You have: tempC
Definition: tempC(x) = x K + stdtemp
defined for x >= -273.15
You have: ~tempC
Definition: ~tempC(tempC) = (tempC +(-stdtemp))/K
defined for tempC >= 0 K
You have: circlearea
Definition: circlearea(r) = pi r^2
r has units m
```

To see the definition of the inverse use the ‘~’ notation. In this case the parameter in the functional definition will usually be the name of the unit. Note that the inverse for ‘tempC’ shows that it requires units of ‘K’ in the specification of the allowed range of values. Nonlinear unit conversions are described in more detail in Defining Nonlinear Units.

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