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Circle Involute Parametric Point Calculator — result sheet
Calculate a point on the involute of a circle from its base radius and unwinding angle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: With t in radians, x=r(cos t+t sin t), y=r(sin t−t cos t).
An involute is traced by the end of a taut line unwound from a circle. The two parametric coordinates show the point in a fixed Cartesian frame whose origin is the base-circle center.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Base-circle radius — length units; minimum 1.0E-6; maximum 1000000000
- Unwinding angle — degrees; minimum 0; maximum 3600
Worked example
| Input | Value |
|---|---|
| Base-circle radius | 10 |
| Unwinding angle | 30 |
x≈11.2782; y≈0.4655 length units.
Assumptions and limits
- The base circle is centered at the origin and the starting tangent is aligned with the positive x direction.
- The angle is converted from degrees to radians before evaluation.
- The curve is ideal and does not model a complete gear profile, clearance, or manufacturing tolerance.
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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