Cartesian to Polar Converter
Convert Cartesian x and y coordinates to polar coordinates (r, θ), in degrees or radians, with a step-by-step derivation and the resulting quadrant.
Input
Output
| Property | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/cartesian-to-polar-converter \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"x": "3.5355",
"y": "3.5355",
"angleUnit": "degrees",
"precision": "4"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `cartesian-to-polar-converter` tool (Cartesian to Polar Converter) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
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src="https://iotools.cloud/embed/cartesian-to-polar-converter/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Cartesian to Polar Converter — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
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Guides
The Cartesian to Polar Converter turns Cartesian coordinates (x, y) — the familiar "over and up" pair used for graphing — into polar coordinates (r, θ), a distance from the origin and an angle. It works in either degrees or radians, and shows the exact formula substitution used to get the answer.
It's built for trigonometry and precalculus students converting homework problems, and anyone working with x/y data (robotics positions, vectors, complex numbers) who needs the equivalent polar form.
How to use it
- Enter x and y, the Cartesian coordinates. Either can be negative or zero.
- Choose whether you want θ reported in degrees or radians.
- Pick how many decimal places to round the result to.
- Read r and θ for the polar coordinates, or the Result table for those plus the coordinates echoed back, the angle in both units, the angle normalized to 0–360°, and which quadrant (or axis) the point falls on.
- Step-by-Step Derivation shows the formula substitution.
Results update automatically as you type. For example, x = 3.5355, y = 3.5355 converts to r = 5, θ = 45° (Quadrant I).
What is the conversion formula?
Given a point in Cartesian form (x, y), the polar coordinates are:
r = √(x² + y²)
θ = atan2(y, x)r is just the Pythagorean distance from the origin. θ uses the two-argument atan2 (rather than a plain arctan(y/x)) so it picks the correct quadrant automatically, including when x = 0.
Why does θ sometimes come out negative?
atan2 returns a principal angle in the range (-180°, 180°] (or (-π, π] in radians) — so a point below the x-axis (negative y) gets a negative angle. The θ normalized (0-360°) row converts that to the more intuitive "measured counterclockwise from the positive x-axis, always positive" convention used in most textbooks.
Degrees or radians?
Pick whichever your target format uses. Radians are the standard unit in most math and physics formulas (a full circle is 2π radians); degrees are more common in everyday and engineering contexts (a full circle is 360°).
For the reverse direction — polar (r, θ) to Cartesian (x, y) — see the Polar to Cartesian Converter.
Privacy
This calculator runs entirely in your browser. Your coordinates are never uploaded, logged, or stored — the computation happens locally on your device.