極座標からデカルト座標への変換器
極座標 (r, θ) をデカルト座標 x および y に変換します。度数またはラジアンで指定でき、段階的な導出と結果の象限が表示されます。
入力
出力
| プロパティ | 値 |
|---|---|
| No data yet | |
このツールを使う他の方法
REST API
curl -X POST https://api.iotools.cloud/v1/tool/polar-to-cartesian-converter \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"radius": "5",
"angle": "45",
"angleUnit": "degrees",
"precision": "4"
}'ご自身のアカウントのキーに差し替えてください。ツールのフィールドがそのままリクエストボディになります——ラッパーはありません。
AIエージェントに依頼する
Use the IOTools `polar-to-cartesian-converter` tool (Polar to Cartesian Converter) on this input:
YOUR_INPUT_HEREIOTools MCPサーバーに接続された任意のエージェントにこれを貼り付け、入力内容を追加してください。
埋め込みウィジェット
<iframe
src="https://iotools.cloud/embed/polar-to-cartesian-converter/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="極座標からデカルト座標への変換器 — 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>ご自身のページに貼り付けるだけ——無料、キー不要、リンクを掲載するだけです。
| API/MCP 1回あたりの費用 | 5クレジットから |
|---|---|
| クレジットが足りませんか? | 料金を見る |
次の方法でも利用可能
ガイド
The Polar to Cartesian Converter turns polar coordinates (r, θ) — a distance from the origin and an angle — into Cartesian coordinates (x, y), the more familiar "over and up" pair used for graphing and most calculations. 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 polar-form data (robotics headings, radar/sonar bearings, complex numbers in polar form) who needs the equivalent x/y point.
How to use it
- Enter r, the radius (distance from the origin) — this can be negative, which points in the opposite direction of θ.
- Enter θ, the angle, and choose whether it's in degrees or radians.
- Pick how many decimal places to round the result to.
- Read x and y for the Cartesian coordinates, or the Result table for those plus the radius/angle echoed back 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, r = 5, θ = 45° converts to x ≈ 3.5355, y ≈ 3.5355 (Quadrant I).
What is the conversion formula?
Given a point in polar form (r, θ), the Cartesian coordinates are:
x = r · cos(θ)
y = r · sin(θ)This follows directly from the definition of sine and cosine on a circle of radius r: θ is measured counterclockwise from the positive x-axis, so r·cos(θ) is the horizontal component and r·sin(θ) is the vertical component of the point.
What does a negative radius mean?
A negative r doesn't move the calculation off the circle — it points the distance in the opposite direction from θ, which is mathematically equivalent to adding 180° to the angle. For example, (r, θ) = (-4, -30°) lands in Quadrant II, the same point you'd get from (4, 150°).
Degrees or radians?
Pick whichever your source data 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°). The calculator's θ (degrees) and θ (radians) result rows show the angle converted to both, regardless of which one you entered.
For the reverse direction — Cartesian (x, y) to polar (r, θ) — or for working with polar-form complex numbers directly, see the Complex Numbers Calculator.
Privacy
This calculator runs entirely in your browser. Your coordinates are never uploaded, logged, or stored — the computation happens locally on your device.