Polar/Rectangular Equation Calculator

Convert equations between polar and rectangular coordinates step by step

The calculator will convert the polar equation to rectangular (Cartesian) and vice versa, with steps shown.

Related calculator: Polar/Rectangular Coordinates Calculator

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Your Input

Convert $$$\left(x - 1\right)^{2} + \left(y - 1\right)^{2} = 2$$$ to polar coordinates.


In polar coordinates, $$$x = r \cos{\left(\theta \right)}$$$ and $$$y = r \sin{\left(\theta \right)}$$$.

Thus, the input can be rewritten as $$$\left(r \sin{\left(\theta \right)} - 1\right)^{2} + \left(r \cos{\left(\theta \right)} - 1\right)^{2} = 2$$$.

Simplify: the input now takes the form $$$r \left(r - 2 \sqrt{2} \sin{\left(\theta + \frac{\pi}{4} \right)}\right) = 0$$$.

Thus, $$$r = 2 \sqrt{2} \sin{\left(\theta + \frac{\pi}{4} \right)}$$$.


$$$\left(x - 1\right)^{2} + \left(y - 1\right)^{2} = 2$$$A in polar coordinates is $$$r = 2 \sqrt{2} \sin{\left(\theta + \frac{\pi}{4} \right)}$$$A.