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2D Rotation Matrix Calculator

Entries of a 2D rotation matrix and an example rotated point.

Compute the entries of a 2-dimensional rotation matrix R(θ) = [[cos θ, −sin θ], [sin θ, cos θ]] and the result of rotating a sample point (x, y) by that angle.

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(θ) = [[cos θ, −sin θ], [sin θ, cos θ]]. Rotated point (x', y') = (x cos θ − y sin θ, x sin θ + y cos θ).

In depth

Compute the entries of a 2-dimensional rotation matrix R(θ) = [[cos θ, −sin θ], [sin θ, cos θ]] and the result of rotating a sample point (x, y) by that angle.