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3-D Rodrigues Rotation Matrix Calculator

R = I + sinθ·K + (1−cosθ)·K², with K = skew(unit-axis).

Compute the nine entries of the 3-D rotation matrix that rotates by angle θ about a unit vector axis (k_x, k_y, k_z), via the Rodrigues formula. Reports the rotation matrix entries directly.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

°

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

R_ij from Rodrigues: R = I + sinθ·K + (1−cosθ)·K², K = skew(k̂).

In depth

Compute the nine entries of the 3-D rotation matrix that rotates by angle θ about a unit vector axis (k_x, k_y, k_z), via the Rodrigues formula. Reports the rotation matrix entries directly.