Polar Coordinates & Curves

Explore coordinates defined by radial distance $r$ and angle $\theta$. Visualize conversions to rectangular coordinates and draw elegant polar curves.

Interactive Sandbox

Concentric Polar Grid

Switch between **Coordinate Explorer** and **Curve Grapher** tabs. Drag on the canvas to set coordinates or select a curve preset to watch coordinates trace out rose petals and cardioids.

Polar Plane: (r, θ) Explorer

Coordinate Formula Mapping

(r, θ) = (2.00, 0.79 rad)

Radius (r) 2.00

Angle (θ in Radians) 0.79 rad (45°)

Drag the coordinates directly on the polar rings to see the rectangular projections.

Algebraic Solver

Conversions step solver

Trace how coordinates map between Rectangular (Cartesian) space and Polar space.

Polar-to-Rectangular Transformation

Conversion Coordinates

Polar Coordinate (r, θ)

(2.00, 45.0°)

Cartesian Coordinate (x, y)

(1.41, 1.41)

Evaluation

Conceptual Quiz

Test your understanding of polar coordinates conversion, rose petal formulas, and cardioids.

Question 1 of 5 Score: 0/0

Convert the polar coordinate (4, π/6) to rectangular coordinates.

Correct Answer!

Explanation text...

Polar Formulas

x = r cos θ | y = r sin θ
r² = x² + y² | θ = atan2(y, x)
Rose petals: k petals if k odd, 2k if k even
Cardioids: Heart-like loops