Enter circular arch data
Example data table
| Scenario | Span | Rise | Thickness | Depth | Radius | Arc Length | Segment Area | Volume |
|---|---|---|---|---|---|---|---|---|
| Walkway entry arch | 8.00 m | 2.00 m | 0.25 m | 0.30 m | 5.00 m | 9.27 m | 11.18 m² | 0.71 m³ |
| Window opening arch | 2.40 m | 0.60 m | 0.12 m | 0.23 m | 1.50 m | 2.78 m | 1.01 m² | 0.10 m³ |
| Decorative gate arch | 3.60 m | 0.90 m | 0.15 m | 0.25 m | 2.25 m | 4.17 m | 2.28 m² | 0.17 m³ |
Formula used
This calculator treats the arch as a circular segment. Keep every length in the same unit before calculating.
R = (L² / 8h) + (h / 2) when span L and rise h are known.h = R - √(R² - (L / 2)²) when radius and span are known.L = 2 × √(2Rh - h²) when radius and rise are known.θ = 2 × asin(L / 2R) for the central angle in radians.Arc Length = R × θSector Area = (R² × θ) / 2Triangle Area = (R² × sin θ) / 2Segment Area = Sector Area - Triangle AreaRing Area = (θ / 2) × (Router² - Rinner²) for a concentric arch ring.Volume = Ring Area × Depth when thickness and barrel width are supplied.How to use this calculator
- Choose the input method that matches your drawing, survey, or measured site dimensions.
- Select one unit and keep all values in that same unit system.
- Enter two known arch values, then optional thickness and depth if you need quantity estimates.
- Click Calculate Arch to display the results above the form.
- Review the computed table and inspect the profile graph.
- Use the export buttons to save CSV or PDF copies.
- Apply the outputs to estimating, drafting, opening checks, and construction planning.
FAQs
1) What does this circular arch calculator measure?
It calculates span, rise, radius, central angle, arc length, segment area, and segment perimeter. If you add thickness and depth, it also estimates arch ring area, soffit area, and approximate material volume.
2) Which inputs should I use first?
Use the values you already know from drawings or field checks. Builders often know span and rise, while fabricators may know radius and angle. The calculator supports multiple input combinations so you can work from existing project information.
3) What is the difference between span and arc length?
Span is the straight horizontal distance between the two springing points. Arc length is the curved distance along the intrados. Because the arch is curved, the arc length is always greater than the straight span.
4) Can this help estimate masonry or concrete quantity?
Yes. Enter ring thickness and barrel width or depth. The calculator estimates the ring area and multiplies it by depth to produce an approximate volume. Add waste, mortar, and project allowances separately during estimating.
5) Which unit should I use?
You can use millimeters, centimeters, meters, inches, or feet. The key rule is consistency. Every dimension must use the same base unit, because the formulas assume a single unit system throughout the calculation.
6) Is this suitable for site layout and shop drawing checks?
It is very useful for quick geometry checks, estimating, and preparing dimensions for layout or drafting. For final project documentation, always confirm tolerances, structural requirements, and code conditions with drawings and engineering review.
7) Why are CSV and PDF exports useful?
CSV works well for spreadsheets, cost planning, and estimate logs. PDF is convenient for approvals, printed records, and sharing with team members. Exporting also reduces manual retyping and helps keep values consistent across documents.
8) Does this replace structural design?
No. This tool handles circular arch geometry and simple quantity outputs only. It does not check loads, reinforcement, support conditions, cracking, thrust, or code compliance. Use a qualified engineer for structural safety and design verification.