3D Point Rotation Calculator

Rotate a point (x, y, z) about the x, y, and z axes by given angles and get the rotated coordinates.

Input

Rotate a point in 3D space about each axis and get the rotated coordinates. Enter rotation angles in degrees.

Point before rotation

x coordinate

y coordinate

z coordinate

Rotation angle per axis (degrees)

About x axis

About y axis

About z axis

Rotations are applied in the order x axis, then y axis, then z axis.

Rotated coordinates

(0, 1, 0)

Original point

(1, 0, 0)

Rotation about x axis

0°

0 rad

Rotation about y axis

0°

0 rad

Rotation about z axis

90°

1.570796 rad

The rotation is computed with rotation matrices in the order x axis, then y axis, then z axis. Positive angles follow the right hand convention.

Each axis rotation is computed with a rotation matrix. Rotation about x affects the y and z components, about y affects z and x, and about z affects x and y; the component along the rotation axis stays unchanged.
The positive direction of rotation follows the right hand convention (counterclockwise when looking toward the positive end of each axis).
Rotations are applied in the order x axis, then y axis, then z axis. The combined rotation is Rz(z angle) Ry(y angle) Rx(x angle), so the input point is first rotated about x, then y, then z. A different order gives a different result.
Angles are entered in degrees and converted to radians internally for the calculation. One degree equals pi divided by 180 radians.

Tell us what you think of this calculator.