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THE FEUTEX TOOLKIT

2D Polar Rotation from a Matrix

Extract the closest proper rotation from an orientation-preserving 2×2 transform.

Math workspace● Runs in your browser
01 Your input
02 Your result
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FormulaAngle = atan2(c-b,a+d)*180/PI; Cosine = (a+d)/hypot(a+d,c-b); Sine = (c-b)/hypot(a+d,c-b)
Sources and model references

Made for real tasks

  • Extract the closest proper rotation from an orientation-preserving 2×2 transform.
Explore step-by-step workflows →

Worked example

Inputs

Matrix a
2 number
Matrix b
-1 number
Matrix c
1 number
Matrix d
3 number

Expected results

Angle
21.80140949 degrees
Cosine
0.9284766909 number
Sine
0.3713906764 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter matrix a, matrix b, matrix c, matrix d.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "a": 2,
  "b": -1,
  "c": 1,
  "d": 3
}

Accuracy and scope

For A=[[a,b],[c,d]] with det(A)>0; does not support reflection transforms.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.