This calculator converts two-dimensional polar coordinates \((R, \theta)\) into rectangular coordinates \((x, y)\).
Using the diagram below, the relationship between rectangular coordinates \((x, y)\) and polar coordinates \((R, \theta)\) is given by:
\[ \begin{aligned} x &= R \cos \theta \\ y &= R \sin \theta \end{aligned} \]The inverse relationships are:
\[ \begin{aligned} R^2 &= x^2 + y^2 \\ \tan \theta &= \frac{y}{x} \end{aligned} \]The correct quadrant of the angle \(\theta\) is determined by the signs of \(x\) and \(y\).
The interactive calculator below computes \(x\) and \(y\) from given values of \(R\) and \(\theta\). The angle \(\theta\) may be entered in either degrees or radians.
Step 1: Enter the angle \(\theta\) and radius \(R\) (with \(R > 0\)).
Step 2: Choose whether \(\theta\) is in degrees or radians, then click Convert.