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
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
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Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun
🔄Last reviewed: May 2026
✓Formula checks are based on standard references and internal QA review.