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Polar Coordinate Converter — result sheet
Convert polar (r, degrees) to rectangular (x, y) and back.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: x = r cos(theta); y = r sin(theta); r = sqrt(x^2+y^2); theta = atan2(y,x).
Polar input uses degrees with the positive x-axis at zero. Reverse conversion uses atan2 so quadrants resolve, normalized to 0-360 degrees.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Direction — 2 choices
- Radius r (or x) — As r for polar input; as x for rectangular input.; minimum -1000000000000; maximum 1000000000000
- Angle in degrees (or y) — As degrees for polar input; as y for rectangular input.; minimum -1000000000000; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Direction | to-rectangular |
| Radius r (or x) | 5 |
| Angle in degrees (or y) | 53.13 |
x = 3, y = 4.
Assumptions and limits
- Angles are degrees, not radians.
- Reverse angle is normalized to 0-360 degrees; origin gives 0.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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