# \curl

Used in physics contexts to represent the curl operator applied to vector fields, with optional delimited arguments

https://texform.dev/latex/commands/curl

## Metadata

| Field | Value |
| --- | --- |
| Topic | [Physics: vectors](https://texform.dev/latex/topics/physics-vectors) |
| Packages | physics |
| Allowed mode | math |
| Tags | mathjax-extension |
| Commonality | low |
| Kind | prefix |

## Syntax

### physics

Argument specification: `d<(,)><[,]><{,}>`

Used in physics contexts to represent the curl operator applied to vector fields, with optional delimited arguments

## Examples

```latex
\curl x
```

[Open in Playground](https://play.texform.dev/?input=%5Ccurl+x)

```latex
\curl{F}
```

[Open in Playground](https://play.texform.dev/?input=%5Ccurl%7BF%7D)

```latex
\curl(F)
```

[Open in Playground](https://play.texform.dev/?input=%5Ccurl%28F%29)

```latex
\curl[F]
```

[Open in Playground](https://play.texform.dev/?input=%5Ccurl%5BF%5D)

## Renderer support

| Package | MathJax | KaTeX | XeTeX |
| --- | --- | --- | --- |
| physics | full | none | full |

## In TeXForm

TeXForm parses this entry as prefix syntax; the package determines its argument specification.

### Expands to (physics)

```latex
\curl
```

→

```latex
\vnabla\crossproduct
```

If followed by `{...}`, it expands to `\vnabla\crossproduct \left\{ ... \right\}` or `\vnabla\crossproduct { ... }` depending on fencing.

## Equivalent forms

```latex
\vnabla\crossproduct
```

approximate. This produces the same operator tokens, but it does not include the helper's special handling for an immediately following ( or [.

```latex
\nabla\times
```

approximate. Close notational equivalent; the physics package uses its own vector nabla/cross-product tokens and also provides auto-open handling for following ( or [.

## See also

- [\\div](https://texform.dev/latex/commands/div)
- [\\divergence](https://texform.dev/latex/commands/divergence)

## Test cases

### physics

| Input | Case | MathJax | KaTeX | XeTeX |
| --- | --- | --- | --- | --- |
| \curl | Positive: baseline | Pass | Fail | Pass |
| \curl (a) | Positive: vary:d[0] | Pass | Fail | Pass |