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Math

Cartesian to Polar Coordinates Calculator

Convert a two-dimensional point into a radius and a quadrant-aware angle.

Exact method explained belowEditable inputs
Calculation notebook
Calculation notebook

The formula and worked example below explain the calculation.

See the method

Enter your values

Runs on your device

Your answer

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter cartesian x, cartesian y.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Radius r = hypot(x,y). For nonzero points θ = atan2(y,x); normalize its degree value into [0,360) so all four quadrants are distinguished.

A WORKED EXAMPLE

Using cartesian x = -3, cartesian y = 4, the result is 5. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

atan2 considers the signs of both coordinates and handles x=0, so it identifies the correct quadrant without dividing by zero.

What to keep in mind

Main result is radius. The origin has radius zero and no unique angle. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.

Common questions

Why use atan2 rather than atan(y/x)?

atan2 considers the signs of both coordinates and handles x=0, so it identifies the correct quadrant without dividing by zero.

How can I check the result?

Radius r = hypot(x,y). For nonzero points θ = atan2(y,x); normalize its degree value into [0,360) so all four quadrants are distinguished. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.

Methodology maintained by ClarityKit. How these tools are built and checked.