Cartesian to Polar Coordinates Calculator
Convert any Cartesian point (x, y) to its polar form (r, θ). Enter x and y to get the radius r and the angle θ in degrees (−180° to 180° and 0° to 360°) and radians (−π to π and 0 to 2π).
Distance from the origin: r = √(x² + y²)
- 1
Square x
3² = 9 - 2
Square y
4² = 16 - 3
x² + y²
9 + 16 = 25 - 4
Radius r = √(x² + y²)
√25 = 5
How does this calculator work?
Given Cartesian point (x, y): radius r = √(x² + y²); angle θ = atan2(y, x) in radians, converted to degrees by multiplying by 180/π. The angle ranges from −180° to 180° (or 0° to 360° when normalised). Both forms describe the same point in the plane.
Formula
How this is calculated
Every point in a plane can be described in two ways: by its Cartesian coordinates (x, y) — how far right and how far up from the origin — or by its polar coordinates (r, θ) — how far from the origin and at what angle. Converting between the two is straightforward algebra.
The radius r is the straight-line distance from the origin to the point, found using the Pythagorean theorem: r = √(x² + y²). The angle θ (theta) is measured anticlockwise from the positive x-axis to the line connecting the origin to the point. It is computed using the atan2 function — a two-argument variant of the inverse tangent that correctly handles all four quadrants and the degenerate cases where x = 0. The result ranges from −180° to 180° (or −π to π radians); adding 360° (or 2π) when θ is negative gives the convention-normalised range 0° to 360° (0 to 2π).
The atan2 convention is used in mathematics, engineering and most programming languages. Be aware that some conventions measure θ from a different axis or in the opposite direction — always check the coordinate-system specification for your application.
Frequently asked questions
atan2(y, x) takes the signs of both arguments to determine the correct quadrant. Plain arctan(y/x) cannot distinguish (1, 1) from (−1, −1) — both give 45° — and fails when x = 0.
The atan2 function returns θ in the range −π to π (−180° to 180°). Adding 2π (360°) to negative values gives the 0 to 2π (0° to 360°) convention. Both describe the same geometric angle.
x = r cos(θ) and y = r sin(θ). This calculator's companion tool — the polar-to-rectangular calculator — performs that inverse conversion.
Also known as
TG we-Calculate Editorial Team. (2026). Cartesian to Polar Coordinates Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cartesian-to-polar-calculator
TG we-Calculate Editorial Team. "Cartesian to Polar Coordinates Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/cartesian-to-polar-calculator.
TG we-Calculate Editorial Team, "Cartesian to Polar Coordinates Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cartesian-to-polar-calculator
@misc{wecalculate_cartesian_to_polar_calculator, title = {Cartesian to Polar Coordinates Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cartesian-to-polar-calculator}}, year = {2026}, note = {TG we-Calculate} }
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