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Coordinates Calculator

Quick answer

This calculator converts Cartesian ↔ polar instantly: r = √(x²+y²), θ = atan2(y, x).

  • Worked example: (3, 4) → r = 5, θ = 53.13°.
  • Free online converter.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

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. Worked example: the point (3, 4) converts to r = √(9+16) = 5 and θ = atan2(4, 3) = 53.13°; back-converting returns exactly (3, 4).

  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

FAQs

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 calculator uses the atan2 function, which picks the correct quadrant automatically, so no manual adjustment is needed wherever the point lies.

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