How to Convert Rectangular to Polar Form (Step-by-Step Guide)
Rectangular to Polar Calculator
What is Rectangular to Polar Conversion?
Rectangular to Polar conversion is the process of transforming coordinates from the Cartesian (x, y) system to Polar (r, θ) form. In the rectangular system, we describe a point’s position using x (horizontal) and y (vertical) distances from the origin. In the polar system, the same point is represented by how far away it is from the origin (the radius, r) and the angle (θ) it makes from the positive x-axis, measured counterclockwise. This conversion is widely used in mathematics, physics, engineering, and computer science because many problems—including those involving circles, waves, and rotation—become easier to analyze in polar coordinates.
Formula or Logic Behind Rectangular to Polar Calculator
To convert rectangular coordinates (x, y) to polar coordinates (r, θ), we use two main formulas:
- Radius: r = √(x² + y²)
- Angle (Theta): θ = arctan(y / x) (usually calculated using atan2 to find the exact quadrant)
Here, r is the distance from the origin to the point (x, y), and θ is the angle (in degrees or radians) from the positive x-axis to the line segment connecting the origin to the point. Our calculator uses these equations and displays both the process and result for maximum clarity.
Rectangular (x, y) to Polar (r, θ) Conversion Table
| x | y | r | θ (degrees) |
|---|---|---|---|
| 1 | 0 | 1.00 | 0.00 |
| 0 | 1 | 1.00 | 90.00 |
| 1 | 1 | 1.41 | 45.00 |
| -1 | 1 | 1.41 | 135.00 |
| -3 | -4 | 5.00 | 233.13 |
| 3 | 4 | 5.00 | 53.13 |
| 5 | 0 | 5.00 | 0.00 |
| 0 | -2 | 2.00 | 270.00 |
Steps to Use the Rectangular to Polar Calculator
- Enter the x (horizontal) and y (vertical) coordinates
- Click on the 'Calculate Polar Coordinates' button
- View the results instantly—see the radius and angle (both in degrees and radians) along with the step-by-step solution
Why Use Vedantu’s Rectangular to Polar Calculator?
Vedantu’s Rectangular to Polar Calculator is designed for simplicity and accuracy. It is mobile-friendly and suitable for students, teachers, engineering aspirants, and professionals. Instantly convert coordinates and see the formula steps explained, making homework, competitive exams, and real-world problem solving much easier. Trusted by students across India, Vedantu calculators ensure fast results and conceptual clarity wherever you are.
Real-life Applications of Rectangular to Polar Converter
Rectangular to polar conversion is used in a variety of fields. For example, in electrical engineering, it’s used to analyze AC circuits and phasors. In physics and robotics, it helps compute movement involving rotation. Architects use it to handle circular or spiral designs. In navigation and mapping, polar coordinates are better suited for describing directions and distances. By understanding both rectangular and polar systems, you can switch perspectives based on the problem—making this calculator useful from classrooms to labs and beyond.
For more understanding on coordinate systems and applications, check out: Coordinate System in Maths, Complex Numbers and Quadratic Equations, Polar Coordinates Explained, Trigonometry Revision Guide, and Argument of Complex Numbers.
FAQs on Rectangular to Polar Calculator – Convert Coordinates Easily
1. How do you convert rectangular coordinates to polar coordinates?
2. What is the formula for converting rectangular to polar coordinates?
3. How to use a rectangular to polar coordinate calculator?
4. What are rectangular and polar coordinates?
5. What is the difference between rectangular and polar coordinates?
6. How do I convert xy to polar form?
7. Convert rectangular coordinates (3, 4) to polar coordinates.
8. Why are rectangular to polar conversions useful?
9. What are some real-world applications of rectangular to polar conversions?
10. How do I handle negative x or y values when converting to polar coordinates?
11. Can I use this calculator for complex numbers?
