Download your PDF
Circular Arch Opening Calculator result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Circular Arch Opening Calculator — result sheet
Calculate the radius, opening area, and curved arch length from a circular-segment opening width and rise.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: R = (c²+4h²)/(8h); θ = 2asin(c/(2R)); segment area = R²(θ−sinθ)/2; arc length = Rθ.
The circular-segment model uses the chord width and rise to derive the circle radius, central angle, opening area, and curved edge length.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Opening width — length units; minimum 1.0E-6; maximum 1000000
- Arch rise — length units; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Opening width | 4 |
| Arch rise | 2 |
Radius = 2; opening area ≈ 6.283 square units; curved length ≈ 6.283 length units.
Assumptions and limits
- Width is the chord and rise is positive; all lengths use one unit.
- The opening is a circular segment with no thickness or side supports included.
- Structural capacity, masonry joints, spring lines, trim, and building-code requirements 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.
No saved result was found. Please run the calculation first, then choose Download again.