Rectangular to Polar Converter

Real-time coordinate conversion tool with advanced features

Real-Time Results
Live Calculation

Rectangular Coordinates Input

Enter X and Y values (Cartesian coordinates)

units
Horizontal distance from origin
units
Vertical distance from origin
Conversion Formula
Radius: r = √(x² + y²)
Angle: θ = atan2(y, x) [radians]
Angle: θ = atan2(y, x) × (180/π) [degrees]

Polar Coordinates Result

Calculated in real-time as you type

Radius (r)
5.00
units (distance from origin)
Calculation: √(3² + 4²) = √25 = 5
Angle (θ)
53.13°
degrees (0° to 360° from positive x-axis)
Quadrant
First Quadrant
Cartesian coordinate quadrant
Equivalent Angle
53.13°, 413.13°, -306.87°
+360°, -360° representations

Coordinate Visualization

Visual representation of rectangular and polar coordinates

Rectangular Point: (3, 4)
Polar Point: (5, 53.13°)
Distance: 5 units

Understanding Rectangular to Polar Coordinate Conversion

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Rectangular to polar coordinate conversion is a fundamental mathematical operation used in various fields including physics, engineering, and computer graphics. This tool provides real-time conversion between these two coordinate systems, helping you visualize and calculate with ease.

How to Use This Tool
  1. Enter the X and Y values in the input section. The tool calculates results in real-time as you type.
  2. View the polar coordinates (radius and angle) in the results section.
  3. Switch between degrees, radians, and gradians for angle measurement using the buttons provided.
  4. Visualize the point on the coordinate plane graph.
  5. Use additional features like history tracking, saving results, and exporting data.
Conversion Formulas

The conversion from rectangular coordinates (x, y) to polar coordinates (r, θ) uses these formulas:

r = √(x² + y²)
θ = atan2(y, x) [in radians]
θ (degrees) = atan2(y, x) × (180/π)

Where atan2 is the two-argument arctangent function that determines the correct quadrant for the angle.

Applications of Polar Coordinates
  • Physics: Analyzing circular motion, electromagnetic fields, and wave functions
  • Engineering: Signal processing, control systems, and antenna radiation patterns
  • Computer Graphics: Creating circular patterns, rotations, and radial gradients
  • Navigation: Determining direction and distance from a reference point

This real-time converter tool simplifies these calculations with instant visual feedback, making it ideal for students, engineers, and professionals working with coordinate systems.

Advanced Features

15+ professional functionalities

Quick Actions

Recent Conversions

Last 5 calculations

(3, 4) → (5, 53.13°)
Just now
First Quadrant
(1, 1) → (1.41, 45.00°)
2 min ago
First Quadrant
(-2, 2) → (2.83, 135.00°)
5 min ago
Second Quadrant
(0, -5) → (5, 270.00°)
10 min ago
On Negative Y-axis
History is saved in your browser's local storage
Calculation Accuracy
High precision calculation with 10 decimal places accuracy
Precision Settings