Convert a point’s rectangular (x, y) coordinates into polar form — a distance from the origin and an angle.
How it works
The distance is r = √(x² + y²) and the angle is θ = atan2(y, x). The point (3, 4) converts to r = 5, θ = 53.13°.
What this does not include
This handles 2D coordinates only. Converting a 3D point (cylindrical or spherical coordinates) needs additional formulas not covered here.
How to use this calculator
- Enter the x and y coordinates.
A worked example
Point (3, 4): r = √(3²+4²) = 5, θ = 53.1301°.
Point (1, 1): r = 1.4142, θ = 45°.
What the variables mean
| Variable | Meaning |
|---|---|
| x, y | Cartesian (rectangular) coordinates |
| r | Distance from the origin |
| θ (theta) | Angle from the positive x-axis, in degrees |
Edge cases worth knowing
The point (3, 4) here is the classic 3-4-5 right triangle — r is just the hypotenuse, found the same way the Pythagorean theorem would.
The origin (0, 0) has no defined angle — r is zero, but there’s no meaningful direction from a point to itself, so the calculator declines to show a result for that case. For the reverse conversion, see this site’s polar-to-rectangular calculator.
Why use atan2 instead of a plain arctangent?
Plain arctangent can’t distinguish between points in opposite quadrants that share the same y/x ratio; atan2 uses the sign of both x and y to return the correct angle across the full circle.
What does polar form make easier?
Rotations and problems with circular or radial symmetry are often much simpler to express in polar form than in x-y coordinates.
Can r ever be negative?
Not in this calculator’s convention — r is a distance, so it’s always zero or positive; the angle θ carries the directional information instead.
