Axis-Angle Calculator

Convert between axis-angle and other rotation representations

Input Type

Axis-Angle Representation

Normalized Axis

(0.000000, 0.000000, 1.000000)

Rotation Angle

90.0000° (1.570796 rad)

Equivalent Representations

Quaternion (w, x, y, z)

(0.707107, 0.000000, 0.000000, 0.707107)

Rotation Vector (axis * angle)

(0.000000, 0.000000, 1.570796)

Rotation Matrix

0.0000-1.00000.0000
1.00000.00000.0000
0.00000.00001.0000

Axis-Angle Formulas

To Quaternion: q = (cos(theta/2), axis * sin(theta/2))

Rotation Vector: r = axis * theta (where theta is in radians)

To Rotation Matrix: Uses Rodrigues rotation formula