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Rectangular to Polar Calculator.

Convert Cartesian x and y coordinates to polar radius and angle.

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Use Cases

Convert Cartesian to Polar for Physics Problems

Use this calculator to quickly convert vector components from rectangular form to magnitude and direction, useful in physics for force, velocity, or displacement vectors.

Example: Convert (3, 4) to polar: r = 5, θ ≈ 53.13°

Plotting Points in Polar Coordinates

When working with polar graphs or complex numbers, convert rectangular coordinates to polar form to easily plot or analyze them.

Example: Convert (-2, 2) to polar: r ≈ 2.83, θ = 135°

Frequently Asked Questions

How do I convert rectangular coordinates to polar coordinates?
Enter the x and y coordinates of the point. The calculator computes r = sqrt(x^2 + y^2) and θ = atan2(y, x) in radians or degrees, depending on your calculator's setting. The result gives the distance from the origin and the angle from the positive x-axis.
What is the range of the angle θ in polar coordinates?
The angle θ is typically given in radians between -π and π (or 0 to 2π) depending on convention. This calculator uses the standard atan2 function, which returns values in the range (-π, π].
Can I use negative coordinates?
Yes, the calculator accepts negative x and y coordinates. The resulting polar coordinates will correctly reflect the quadrant of the point, with the angle adjusted accordingly.

Tips & Common Mistakes

Tips

  • Ensure you enter the x and y coordinates as numbers; the calculator accepts negative values and decimals.
  • Check whether your calculator outputs the angle in degrees or radians, and adjust your interpretation accordingly.
  • For points on the axes, the angle is straightforward: (positive x) gives 0°, (negative x) gives 180°, (positive y) gives 90°, (negative y) gives 270°.
  • Use the polar coordinates to verify your manual calculations or to explore the relationship between the two coordinate systems.

Common Mistakes to Avoid

  • Forgetting to consider the quadrant when manually calculating the angle; this calculator automatically handles it with atan2.
  • Confusing the order of coordinates: always enter x first, then y.
  • Assuming the angle is always in degrees; check the calculator's output unit.

Last updated: August 13, 2026