Inputs
Example Data
Click Use to populate the form with an example.
| Units | Span | Rise | Ring t | Depth | Density | Voussoirs | |
|---|---|---|---|---|---|---|---|
| Metric | 2.400 m | 0.600 m | 0.250 m | 0.450 m | 2400 kg/m³ | 10 | |
| Metric | 3.000 m | 0.800 m | 0.300 m | 0.350 m | 2300 kg/m³ | 12 | |
| Imperial | 8.000 ft | 2.000 ft | 0.667 ft | 1.000 ft | 145 lb/ft³ | 12 |
Quick Notes
R = L²/(8h) + h/2
θ = 2·arcsin(L/(2R))
s = R·θ
Aseg = (R²/2)(θ − sinθ)
Results
Formulas Used
- Radius (midline):
R = L²/(8h) + h/2 - Central angle:
θ = 2·arcsin(L/(2R)) - Arc length (midline):
s = R·θ(θ in radians) - Segment area (midline):
A = (R²/2)(θ − sinθ)
- Intrados / Extrados radii:
Ri = R − t/2,Ro = R + t/2 - Voussoir wedge angle:
Δθ = θ / n(n = count) - Volume:
V = A · depth - Weight:
W = V · ρ(ρ = density)
All geometry is for a circular segment. Thickness is treated as concentric about the midline. Engineering checks, thrust, and masonry detailing are outside this scope.
How to Use
- Select your preferred unit system.
- Enter span and rise. Both must be positive.
- Optionally add ring thickness, wall depth, density, and voussoirs.
- Click Calculate to compute geometry, volume, and weight.
- Review the summary and, if applicable, the voussoir breakdown table.
- Use Download CSV or Download PDF to export.
- Print a formatted report with the Print button.
FAQs
Only span and rise are essential. From these, the circle radius, central angle, and arc length are determined for a circular segment.
When ring thickness is given, intrados and extrados radii are taken as midline radius minus/plus half the thickness. Arc lengths follow the same central angle.
Yes. Provide wall depth and material density. The calculator computes segment volume and multiplies by density to estimate weight.
Voussoirs are wedge-shaped blocks forming the ring. If you provide a count, the tool splits the central angle evenly and reports per‑block face lengths.
No. This tool reports geometry, volumes, and weights only. For thrust lines, reinforcement, and code checks, consult a structural engineer.
Reference: Span–Rise–Radius & Angle
Typical Material Densities for Weight Estimation
| Material | Density (kg/m³) | Density (lb/ft³) | Notes |
|---|---|---|---|
| Clay brick masonry | 1800–2000 | 112–125 | Varies with voids and mortar content. |
| Concrete (normal weight) | 2300–2400 | 143–150 | Use 2400 kg/m³ for conservative estimates. |
| Limestone | 2200–2500 | 137–156 | Natural stone variability by quarry. |
| Sandstone | 2000–2300 | 125–143 | Often used in historic arches. |
| Granite | 2600–2700 | 162–168 | Dense; increases weight estimates noticeably. |
Proportions & Rules‑of‑Thumb (Geometry Only)
| Arch type | Typical rise/span | Ring thickness t/span | Voussoir count | Notes |
|---|---|---|---|---|
| Semicircular | 0.50 | 0.06–0.12 | 9–15 | Crown at half span; geometry stable and common. |
| Segmental (moderate) | 0.15–0.35 | 0.06–0.10 | 9–17 | Lower rise for openings; check thrust separately. |
| Low‑rise segment | 0.10–0.20 | 0.08–0.12 | 11–19 | Higher horizontal thrusts; structural design required. |