# Polar Coordinates Calculator

URL: https://speedycalculator.com/calculators/math/cartesian-to-polar/
Last updated: 2026-10-25

> This calculator converts Cartesian coordinates (x, y) to polar coordinates (r, θ). It is used in physics, engineering, navigation and complex numbers.

## Inputs

- x
- y

## Results

- Radius r
- Angle θ
- Angle θ (radians)

## Formula

```
r = √(x² + y²)
θ = atan2(y, x)
```

## Explanation

Polar coordinates describe a point by its distance from the origin and its angle from the positive x-axis.

### How to use the Polar Coordinates Calculator

- **x**
- **y**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Pythagoras gives r and the two-argument arctangent gives the angle in the correct quadrant.

### Inputs explained

FieldWhat to enterxA numberyA number

### What each result means

- **Radius r** = sqrt([x]^2 + [y]^2)
- **Angle θ** = deg(atan2([y], [x]))
- **Angle θ (radians)** = atan2([y], [x])

### Example values

How the main result changes when **x** changes and everything else stays at the example values above:

xRadius r-1.54.272-2.254.5894-35-3.755.4829-4.56.0208-67.2111

## Worked example

Inputs — x: -3; y: 4.

Results — **Radius r = 5**; Angle θ = 126.8699 °; Angle θ (radians) = 2.214297.

## FAQ

**How do I convert back?**
x = r cos θ, y = r sin θ.

**Why atan2 instead of atan?**
atan2 uses the signs of x and y to place the angle in the right quadrant.

**What formula does the Polar Coordinates Calculator use?**
r = √(x² + y²).