# Using the Formulas Element

This topic describes VML, a feature that is deprecated as of Windows Internet Explorer 9. Webpages and applications that rely on VML should be migrated to SVG or other widely supported standards.

**Note** As of December 2011, this topic has been archived. As a result, it is no longer actively maintained. For more information, see Archived Content. For information, recommendations, and guidance regarding the current version of Windows Internet Explorer, see Internet Explorer Developer Center.

In this topic, we will illustrate how to use the <formulas> sub-element to define an adjustable path for a shape.

You can place the <formulas> sub-element inside <shape> or <shapetype> to define formulas that can vary the path of a shape. Inside the <formulas> sub-element, one **f** sub-element defines one formula so that one value is evaluated based upon that formula. For example, the formula, `<v:f eqn="prod 10 4 5"/>`

defines a value that is equivalent to "10 x 4 / 5".

You can place many **f** sub-elements inside one <formulas> sub-element. Formulas can reference the values that are defined earlier in other formulas within the same <formulas> sub-element. The value that is defined in the first formula can be referred to as @0, the value that is defined in the second formula can be referred to as @1, and so on.

In addition, you can specify the **adj** property attribute of the <shape> element, such as adj="100, 200, 150". Inside the <formulas> element, you can then reference those values in the **adj** list. The first value (100) in the **adj** list can be referred to as #0, the second value (200) can be referred to as #1, and so on.

For example, to draw a smiling face, you can type the following VML representation:

```
<v:shape style='width:1in;height:1in;' strokecolor="red"
strokeweight="2pt" coordsize="21600,21600" adj="17520"
path="m10800,0qx0,10800,10800,21600,21600,10800,10800,0xe
m7340,6445qx6215,7570,7340,8695,8465,7570,7340,6445xnfe
m14260,6445qx13135,7570,14260,8695,15385,7570,14260,6445xnfe
m4960@0c8853@3,12747@3,16640@0nfe">
<v:formulas>
<v:f eqn="sum 33030 0 #0"/>
<v:f eqn="prod #0 4 3"/>
<v:f eqn="prod @0 1 3"/>
<v:f eqn="sum @1 0 @2"/>
</v:formulas>
</v:shape>
```

`adj="17520"`

defines a value (= 17520). This value can be referenced as #0.- The first formula,
`<v:f eqn="sum 33030 0 #0"/>`

, defines the value (= 33030 + 0 - #0). This value can be referenced as @0. - The second formula,
`<v:f eqn="prod #0 4 3"/>`

, defines the value (= #0 * 4 / 3). This value can be referenced as @1. - The third formula,
`<v:f eqn="prod @0 1 3"/>`

, defines the value (= @0 * 1 / 3). This value can be referenced as @2. - The fourth formula,
`<v:f eqn="sum @1 0 @2"/>`

, defines the value (=@1 + 0 -@2). This value can be referenced as @3. - Inside the <path> element, the values defined in the first (@0) and the fourth (@3) formulas are used to determine the outline of the shape.

If you change the **adj** list, such as `adj="20000"`

, the values of the formulas that reference the **adj** list will be changed as well, affecting the smiling face as follows:

```
<v:shape style='width:1in;height:1in;' strokecolor="red"
strokeweight="2pt" coordsize="21600,21600" adj="20000"
path="m10800,0qx0,10800,10800,21600,21600,10800,10800,0xe
m7340,6445qx6215,7570,7340,8695,8465,7570,7340,6445xnfe
m14260,6445qx13135,7570,14260,8695,15385,7570,14260,6445xnfe
m4960@0c8853@3,12747@3,16640@0nfe">
<v:formulas>
<v:f eqn="sum 33030 0 #0"/>
<v:f eqn="prod #0 4 3"/>
<v:f eqn="prod @0 1 3"/>
<v:f eqn="sum @1 0 @2"/>
</v:formulas>
</v:shape>
```

For more information about this element, see the VML specification .

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Build date: 2/7/2012