rotate3d()
==========

 The **`rotate3d()`** CSS function defines a transformation that rotates an element around a
 fixed axis in 3D space, without deforming it. Its result is a `<transform-function>` data type.

Try it
------

 In 3D space, rotations have three degrees of freedom, which together describe a single axis of rotation. The axis of
 rotation is defined by an [x, y, z] vector and pass by the origin (as defined by the `transform-origin`
 property). If, as specified, the vector is not *normalized* (i.e., if the sum of the square of its three
 coordinates is not 1), the user agent will normalize it internally. A non-normalizable vector, such as
 the null vector, [0, 0, 0], will cause the rotation to be ignored, but without invalidating the whole CSS property.


**Note:** Unlike rotations in the 2D plane, the composition of 3D rotations is usually
 not commutative. In other words, the order in which the rotations are applied impacts the result.


Syntax
------

 The amount of rotation created by `rotate3d()` is specified by three `<number>`s and
 one `<angle>`. The `<number>`s represent the x-, y-, and z-coordinates of the
 vector denoting the axis of rotation. The `<angle>` represents the angle of rotation; if positive,
 the movement will be clockwise; if negative, it will be counter-clockwise.


```css
rotate3d(x, y, z, a)
```

### Values

`x`

 Is a `<number>` describing the x-coordinate of the vector denoting the axis of rotation which
 can be a positive or negative number.


`y`

 Is a `<number>` describing the y-coordinate of the vector denoting the axis of rotation which
 can be a positive or negative number.


`z`

 Is a `<number>` describing the z-coordinate of the vector denoting the axis of rotation which
 can be a positive or negative number.


`a`

 Is an `<angle>` representing the angle of the rotation. A positive angle denotes a clockwise
 rotation, a negative angle a counter-clockwise one.




|  |  |
| --- | --- |
| Cartesian coordinates on ℝ^2 | 
 This transformation applies to the 3D space and can't be represented on
 the plane.
  |
| Homogeneous coordinates on ℝℙ^2 |
| Cartesian coordinates on ℝ^3 | 

(

1
+
(
1
−
cos
(
a
)
)
(

x
2

−
1
)

z
⋅
sin
(
a
)
+
x
y
(
1
−
cos
(
a
)
)

−
y
⋅
sin
(
a
)
+
x
z
(
1
−
cos
(
a
)
)

−
z
⋅
sin
(
a
)
+
x
y
(
1
−
cos
(
a
)
)

1
+
(
1
−
cos
(
a
)
)
(

y
2

−
1
)

x
⋅
sin
(
a
)
+
y
z
(
1
−
cos
(
a
)
)

y
⋅
sin
(
a
)
+
x
z
(
1
−
cos
(
a
)
)

−
x
⋅
sin
(
a
)
+
y
z
(
1
−
cos
(
a
)
)

1
+
(
1
−
cos
(
a
)
)
(

z
2

−
1
)

)

\begin{pmatrix}1 + (1 - \cos(a))(x^2 - 1) & z\cdot \sin(a) + xy(1 - \cos(a)) & -y\cdot \sin(a) + xz(1 - \cos(a))\\-z\cdot \sin(a) + xy(1 - \cos(a)) & 1 + (1 - \cos(a))(y^2 - 1) & x\cdot \sin(a) + yz(1 - \cos(a))\\y\cdot \sin(a) + xz(1 - \cos(a)) & -x\cdot \sin(a) + yz(1 - \cos(a)) & 1 + (1 - \cos(a))(z^2 - 1)\end{pmatrix}

 |
| Homogeneous coordinates on ℝℙ^3 | 

(

1
+
(
1
−
cos
(
a
)
)
(

x
2

−
1
)

z
⋅
sin
(
a
)
+
x
y
(
1
−
cos
(
a
)
)

−
y
⋅
sin
(
a
)
+
x
z
(
1
−
cos
(
a
)
)

0

−
z
⋅
sin
(
a
)
+
x
y
(
1
−
cos
(
a
)
)

1
+
(
1
−
cos
(
a
)
)
(

y
2

−
1
)

x
⋅
sin
(
a
)
+
y
z
(
1
−
cos
(
a
)
)

0

y
⋅
sin
(
a
)
+
x
z
(
1
−
cos
(
a
)
)

−
x
⋅
sin
(
a
)
+
y
z
(
1
−
cos
(
a
)
)

1
+
(
1
−
cos
(
a
)
)
(

z
2

−
1
)

0

0

0

0

1

)

\begin{pmatrix}1 + (1 - \cos(a))(x^2 - 1) & z\cdot \sin(a) + xy(1 - \cos(a)) & -y\cdot \sin(a) + xz(1 - \cos(a)) & 0\\-z\cdot \sin(a) + xy(1 - \cos(a)) & 1 + (1 - \cos(a))(y^2 - 1) & x\cdot \sin(a) + yz(1 - \cos(a)) & 0\\y\cdot \sin(a) + xz(1 - \cos(a)) & -x\cdot \sin(a) + yz(1 - \cos(a)) & 1 + (1 - \cos(a))(z^2 - 1) & 0\\0 & 0 & 0 & 1\end{pmatrix}

 |

Examples
--------

### Rotating on the y-axis

#### HTML


```html
<div>Normal</div>
<div class="rotated">Rotated</div>
```


#### CSS


```css
body {
  perspective: 800px;
}

div {
  width: 80px;
  height: 80px;
  background-color: skyblue;
}

.rotated {
  transform: rotate3d(0, 1, 0, 60deg);
  background-color: pink;
}
```


#### Result

### Rotating on a custom axis

#### HTML


```html
<div>Normal</div>
<div class="rotated">Rotated</div>
```


#### CSS


```css
body {
  perspective: 800px;
}

div {
  width: 80px;
  height: 80px;
  background-color: skyblue;
}

.rotated {
  transform: rotate3d(1, 2, -1, 192deg);
  background-color: pink;
}
```


#### Result

Specifications
--------------

| Specification |
| --- |
| CSS Transforms Module Level 2 # funcdef-rotate3d |

Browser compatibility
---------------------

BCD tables only load in the browser with JavaScript enabled. Enable JavaScript to view data.

See also
--------

* `transform` property
* `rotate` property
* `<transform-function>`