# Polar Coordinates Calculator

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## What is Polar Coordinates Calculator?

A Polar Coordinates Calculator is a tool used to calculate the polar coordinates of a point in a two-dimensional plane, given its rectangular (Cartesian) coordinates. Polar coordinates are a way of describing the position of a point in terms of its distance from the origin (radius) and the angle it forms with the positive x-axis (angle or azimuth).

The Polar Coordinates Calculator typically requires the user to input the x and y coordinates of the point, and then calculates the corresponding radius and angle. The calculator can display the results in either degrees or radians, depending on the user’s preference.

**Formula for Polar Coordinates**

The formula for converting rectangular (Cartesian) coordinates (x, y) to polar coordinates (r, θ) is:

**r = √(x² + y²) **

**θ = arctan (y/x)**

**where:**

- r is the distance from the origin to the point (also known as the radius)
- θ is the angle formed between the positive x-axis and the line connecting the origin and the point (also known as the angle or azimuth)
- x is the x-coordinate of the point
- y is the y-coordinate of the point
- arctan is the inverse tangent function

**Example Calculation**

Suppose we have a point P with coordinates (2, 3) in a Cartesian plane. We want to find its polar coordinates (r, θ).

First, we can calculate the radius r as: r = √(2² + 3²) = √13 ≈ 3.605

Then, we can calculate the angle θ as: θ = arctan (3/2) ≈ 56.31°

Therefore, the polar coordinates of the point P are approximately (3.605, 56.31°).

**How to use the Polar Coordinates Calculator**

To use the Polar Coordinates Calculator, follow these steps:

- Input the x and y coordinates of the point you want to convert to polar coordinates.
- Click the “Calculate” button to execute the calculation.
- The calculator will display the resulting radius and angle (in either degrees or radians).

**FAQs**

**What is the difference between Cartesian and polar coordinates?**

Cartesian coordinates describe the position of a point in terms of its x and y coordinates, whereas polar coordinates describe the position in terms of its radius and angle.

**How do you convert polar coordinates to Cartesian coordinates?**

To convert polar coordinates (r, θ) to Cartesian coordinates (x, y), use the following formulas: x = r * cos(θ) y = r * sin(θ)

**What is the range of values for polar coordinates?**

The radius (r) is always a positive value, and the angle (θ) can range from 0 to 360 degrees (or 0 to 2π radians), depending on the convention used.