Polar Coordinates Calculator

Convert the a point in the Cartesian plane to it’s 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.

How to calculate polar coordinates

Polar coordinates are expressed as two values. One being 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.

r = √(x² + y²)

θ = arctan (y/x)

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 millennium. Coming about, as most math related concepts are, through a Greek scientist. More specifically a Greek astronomer who was looking to use functions to calculate the position of stars.

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

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