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Cycloid Arch Geometry Calculator — result sheet
Calculate ideal height, arch length, and area for one cycloid arch generated by a rolling circle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: One arch height=2r; arch length=8r; area under one arch=3πr².
The page uses the standard one-arch cycloid relationships and reports the geometric quantities with the radius kept visible.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Generating-circle radius — minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Generating-circle radius | 2 |
Height =4; arch length =16; area ≈37.699.
Assumptions and limits
- The curve is a standard cycloid generated by a circle rolling without slip.
- Area means the region under one arch above the baseline.
- Truncation, cusps, orientation, and nonuniform rolling are not modeled.
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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