Cartesian To Polar Coordinates Calculator

Work out cartesian to polar coordinates instantly with clear inputs, formula shown and shareable results.

About Cartesian To Polar Coordinates Calculator

Polar coordinates give a distance from the origin and an angle. The radius is √(x² + y²) and the angle uses atan2 rather than plain arctan, so it lands in the correct quadrant.

Formula

Cartesian to polar

r = √(x² + y²), θ = atan2(y, x)

Worked example

With the default values below, Cartesian To Polar Coordinates Calculator returns Radius r of 5.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

x coordinate: -3
y coordinate: 4

Results

Radius r: 5.00000000
Angle θ (−180° to 180°): 126.869898 °
Angle θ (0° to 360°): 126.869898 °
Angle in radians: 2.21429744

Step by step

1Values used
2Cartesian to polar
3Radius r= 5.00000000
4Angle θ (−180° to 180°)= 126.869898 °
5Angle θ (0° to 360°)= 126.869898 °
6Angle in radians= 2.21429744

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For (−3, 4)?

r = 5 and θ = atan2(4, −3) ≈ 126.8698976°, correctly in the second quadrant.

Why not use arctan(y/x)?

Because it loses the sign information: (−3, 4) and (3, −4) give the same ratio but lie in opposite quadrants.