Polar Coordinates Calculator: [Rectangular to Polar, Polar to Rectangular]

Here’s what G-Wizard’s Polar Coordinates Calculator looks like:

polar coordinates calculator

Free G-Wizard Polar Coordinates Calculator…

As you can see, the Polar to Rectangular Calculator is just one of a number of useful calculators included with the software and free for you to use.

Download our G-Wizard Calculator to get the free Polar Coordinates Calculator. You can use this calculator (and many of the others) in G-Wizard for life just by signing up for our 30-day trial. That’s right–most of the calculators can still be used after the trial expires.

To sign up, simply visit the G-Wizard page or click this button:

Get Me the Free G-Wizard Trial!

Math behind Converting Polar to Rectangular Coordinates

Converting from Polar to Rectangular (also called Cartesian) coordinates is easy to do. Refer to this diagram:

polar to rectangular coordinate conversion

Variables used in polar to rectangular coordinate conversions…

The variables used in polar to rectangular coordinate conversion are:

x: The X-Axis coordinate

y: The Y-Axis coordinate

r: The radius or distance on the polar vector

Theta (Greek character): The angle from the X-Axis in a counter-clockwise direction

Equation to Convert Polar to Rectangular Coordinates

Given r and Theta, we can find x and y to convert from Polar to Rectangular coordinates as follows:

x = r Cos( Theta )

y = r Sin( Theta )

Equation to Convert Rectangular to Polar Coordinates

If we know x and y, we can find r and Theta to convert from Rectangular to Polar coodinates as follows:

r = SQRT( x * x + y * y )

Theta = arctan( y / x )

Video on How to Convert With a Hand-Held Calculator

Polar Coordinates Application to CNC and Bolt Circles

Programming a CNC machine in polar coordinates can simplify a lot of problems.  Take bolt circles for example.  They’re very easy to do in Polar Coordinates.  The radius of the circle is the polar radius.  And the angle between holes is just 360 degrees divided by the number of holes.

Whether you want to program the bolt circle directly in polar or use a polar coordinates calculator like this one to crank out the normal Cartesian (rectangular) coordinates, bolt circles are a lot easier when done this way.

For more on polar coordinate g-code programming see our article:

Other Resources

More detail, examples, and a quiz on Rectangular to Polar Conversions


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