Cartesian to Polar Calculator - Convert Coordinates Instantly

Polar Coordinates Calculator - Convert Cartesian and Polar

Our Polar Coordinates Calculator lets you easily convert between Cartesian (rectangular) and Polar coordinate systems. Whether you're studying trigonometry, engineering, or physics, this free tool saves time and ensures accurate calculations.

What Are Polar Coordinates?

Polar coordinates represent a point using a radius and an angle, rather than the standard x and y coordinates. They are written in the form:

\((r, \theta)\)

- \(r\) is the distance from the origin
- \(\theta\) (theta) is the angle measured in degrees or radians from the positive x-axis

Polar to Cartesian Conversion

To convert polar coordinates to Cartesian:

\(x = r \times \cos(\theta)\) \(y = r \times \sin(\theta)\)

Cartesian to Polar Conversion

To convert Cartesian coordinates to polar:

\(r = \sqrt{x^{2}+y^{2}}\) \(\theta = a \tan2(y, x)\)

Example

Convert (3, 4) from Cartesian to Polar:

\(r = \sqrt{(3^{2}+4^{2})} = 5\) \(\theta = a \tan2(4, 3) \approx {53.13}^\circ \) \(Polar: (5, 53.13^\circ )\)

Why Use a Polar Coordinates Calculator?

• Accurate conversions between polar and rectangular coordinates
• Handles degrees or radians
• Useful for vector analysis and complex numbers
• Perfect for students, teachers, engineers, and professionals

Applications

Polar coordinates are used in:

• Mathematics: Trigonometry, complex numbers, graphing
• Physics: Motion in circular paths, electromagnetism
• Engineering: Control systems, robotics
• Computer graphics: Plotting curves, animations

How to Use This Calculator

1. Select the conversion direction (Cartesian \(\rightarrow\) Polar or Polar \(\rightarrow\) Cartesian)
2. Enter the values for \(x\) and \(y\) or \(r\) and \(\theta\)
3. Click “Calculate