Rectangular to Polar Coordinates logo
Rectangular to Polar Coordinates

Rectangular ↔ Polar Coordinates

Convert between (x, y) and (r, θ) with quadrant-aware angles and adjustable precision.

Precision: 4
Angle:

Rectangular → Polar

Enter x and y to get r and θ.

r
5
θ (degrees)
53.1301

Polar → Rectangular

Enter r and θ to get x and y.

Tip: If your θ is in radians, switch the Angle mode above.

x
3
y
4

How rectangular to polar coordinates conversion works

For a point (x, y), the polar radius is r = √(x² + y²) and the angle is θ = atan2(y, x). Using atan2 ensures the correct quadrant and handles x = 0 safely.

  • Degrees ↔ Radians: deg = rad × (180/π), rad = deg × (π/180)
  • Polar → Rectangular: x = r·cos(θ), y = r·sin(θ)
  • We normalize θ to [0, 360) for clarity.

Frequently Asked Questions

How do I convert rectangular coordinates to polar coordinates?
Compute r = √(x² + y²) and θ = atan2(y, x). The function atan2 considers the signs of x and y to return the correct angle for all quadrants.
How to change polar coordinates into rectangular coordinates?
Use x = r·cos(θ) and y = r·sin(θ). If your θ is in degrees, convert it to radians before calling trig functions, or switch the calculator’s angle mode.
What is the R θ in polar coordinates?
r is the distance from the origin (non-negative). θ is the angle from the positive x-axis, measured counterclockwise. We display θ normalized for consistency.
What is the formula for converting to Polar Form?
From rectangular (x, y) → polar (r, θ): r = √(x² + y²), θ = atan2(y, x).