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
| Field | What to enter |
|---|---|
| x | A number |
| y | A 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:
| x | Radius r |
|---|---|
| -1.5 | 4.272 |
| -2.25 | 4.5894 |
| -3 | 5 |
| -3.75 | 5.4829 |
| -4.5 | 6.0208 |
| -6 | 7.2111 |
Formula
r = √(x² + y²)θ = atan2(y, x)Worked example
Inputs — x: -3; y: 4.
Results — Radius r = 5; Angle θ = 126.8699 °; Angle θ (radians) = 2.214297.
Frequently asked questions
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).