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2D Point Rotation Calculator — result sheet
Rotate a Cartesian point about the origin and report its new coordinates, radius, and direction.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: x′ = x cosθ - y sinθ; y′ = x sinθ + y cosθ; radius = √(x′²+y′²).
The standard counterclockwise rotation matrix transforms the point around the origin. Rotation preserves its distance from the origin, which is shown as a useful check.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Point x — minimum -1000000000; maximum 1000000000
- Point y — minimum -1000000000; maximum 1000000000
- Counterclockwise rotation — °; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Point x | 3 |
| Point y | 4 |
| Counterclockwise rotation | 90 |
Rotated point: (-4, 3); radius: 5 units.
Assumptions and limits
- The point is rotated in a flat Cartesian plane about the origin, not about an arbitrary center.
- Positive angles rotate counterclockwise and negative angles rotate clockwise.
- The input and output coordinates use the same unit and angle input is in degrees.
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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