Convert a point in the Cartesian plane to its equal polar coordinates with this polar coordinate calculator. Polar coordinates also take place in the x-y plane but are represented by a radius and angle as shown in the diagram below.

Polar Coordinates Formula

The following formulas are used to convert polar coordinates from Cartesian coordinates.

r = √(x² + y²)

θ = arctan (y/x)

  • Where r is the radius
  • x and y are the coordinate points
  • θ is the angle

Polar Coordinates Definition

Polar coordinates are expressed as two values. One is a radius, and the other being the angle. The radius is a function of the x and y coordinates and is the angle. The following formulas are used to calculate the radius and angle.

How to calculate polar coordinates

As you can see from the formulas the radius is a function of the square root of the sum of the x and y coordinates squared. In other words, the radius length acts as the hypotenuse on a triangle with lengths x and y.

The angle that describes the rotation of the radius is equal to an angle in a triangle with sides x and y, and hypotenuse r. This is also known as the reference angle.

More about Polar Coordinates

Polar coordinates have been around for a millennium. Coming about, as most math-related concepts are, through a Greek scientist. More specifically a Greek astronomer was looking to use functions to calculate the position of stars.

The angle in polar coordinates is oftentimes described by the Greek letter theta and is measured in either degrees or radians. The radius denoted with r is typically measured in a unitless measure, but some distance measures such as inches or meters could be used.


What are polar coordinates?

Polar coordinates are a way of displaying the location of a point in the 2-dimensional plane using a radius of a circle and angle as measure from the x-axis.

What are Cartesian coordinates?

Cartesian coordinates are a way of display the location of a point in the 2 dimension plane using an X and Y coordinate.

For more math related calculators, click here.