Coordinates Calculator

Convert between different coordinate systems like Cartesian and Polar.

Inputs

Coordinate Systems

The Cartesian system specifies a point uniquely in a plane by a pair of numerical coordinates. The Polar system specifies a point by a distance from a fixed point and an angle from a fixed direction.

Formulas

  • x = r cos(θ), y = r sin(θ)
  • r = √(x² + y²), θ = atan2(y, x)

Results

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How Coordinates Calculator Works

r = sqrt(x² + y²), theta = atan2(y, x) for Cartesian to Polar

Convert points between Cartesian (x, y) and Polar (r, theta) coordinate systems using trigonometric relationships.

  1. 1

    Step 1

    Select conversion direction

  2. 2

    Step 2

    Enter coordinates in the source system

  3. 3

    Step 3

    Choose angle unit (degrees or radians)

  4. 4

    Step 4

    View converted coordinates

Use Cases

Physics problems involving circular motion

Engineering and robotics

Navigation and mapping

Computer graphics and game development

Tips

  • 1

    Cartesian coordinates are named after Descartes

  • 2

    360 degrees = 2 pi radians

  • 3

    The polar system is useful for circular shapes and rotational motion

  • 4

    Pay attention to the quadrant when calculating angles

  • 5

    The Cartesian point (0,0) corresponds to r=0 in polar

Common Mistakes

  • Forgetting to convert angles between degrees and radians

  • Not paying attention to the correct quadrant when calculating the angle

  • Confusing sin and cos in conversion formulas

  • Entering a negative value for the radius r

Frequently Asked Questions

What is the difference between Cartesian and polar systems?
Cartesian defines a point using two perpendicular distances (x, y), while polar defines it using a distance from the center (r) and an angle from the positive axis (theta).
How do I convert from degrees to radians?
Radians = degrees × (pi/180). For example: 90 degrees = 90 × (pi/180) = pi/2 radians.
When is the polar system better?
When dealing with circular motion, waves, rotation, or any phenomenon involving angles and distances from a center.
What happens at the point (0,0)?
The point (0,0) in Cartesian corresponds to r=0 in polar. The angle is undefined because the point is at the center.
Why pay attention to the quadrant when calculating the angle?
The inverse tan function gives an angle only in the first and fourth quadrants. You must manually adjust the result if the point is in the second or third quadrant.

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