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.

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.

rotate3d(x, y, z, a)

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	$\left(\begin{array}{ccc}1+(1-cos(a\left)\right)(x^2-1)& z·sin\left(a\right)+xy(1-cos(a\left)\right)& -y·sin\left(a\right)+xz·(1-cos(a\left)\right)\\ -z·sin\left(a\right)+xy·(1-cos(a\left)\right)& 1+(1-cos(a\left)\right)(\mathrm{y2}-1)& x·sin\left(a\right)+yz·(1-cos(a\left)\right)\\ ysin\left(a\right)+\mathrm{xz}(1-cos(a\left)\right)& -xsin\left(a\right)+\mathrm{yz}(1-cos(a\left)\right)& 1+(1-cos(a\left)\right)(\mathrm{z2}-1)& t\\ 0& 0& 0& 1\end{array}\right)$
Homogeneous coordinates on ℝℙ^3

HTML

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

CSS

body {
  perspective: 800px;
}

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

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

Result

HTML

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

CSS

body {
  perspective: 800px;
}

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

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

Result

• transform property
• rotate property
• <transform-function>