Vertex Length Calculator: Global Geometry Tool
The most accurate vertex length calculator for parabolic, circular, and elliptical arches — used in architecture, engineering, and optics worldwide.
"The vertex defines the curve." — Geometry Principle
How the Vertex Length Calculator Works
Our vertex length calculator uses exact formulas:
- Parabolic: S = H (vertex length = rise)
- Circular: S = R − √(R² − (C/2)²)
- Radius: R = (C²/4 + H²) / (2H)
- Arc Length: L = 2R × arcsin(C/(2R))
Understanding Vertex Length Calculator Results
You get:
- Vertex Length (Sagitta)
- Arc Length
- Radius of Curvature
- Shape Classification
Why Use This Vertex Length Calculator?
Trusted globally:
- All arch shapes
- Imperial & Metric
- Real-time validation
- Arc & radius output
- Mobile-optimized
Real Vertex Length Calculator Examples
- 100m chord, 20m rise (parabolic): → 20m vertex
- 10ft chord, 2ft rise (circular): → 1.25ft sagitta
- 50in mirror, 5in rise: → 62.5in radius
- Bridge arch: → 125m arc length
Parabolic vs Circular vs Elliptical
- Parabolic: Constant focal length
- Circular: Uniform curvature
- Elliptical: Two foci, aesthetic
Applications of Vertex Length
- Architecture: Vaults, domes
- Bridges: Arch design
- Optics: Parabolic mirrors
- Roofing: Curved structures
Get Started with Vertex Length Calculator
- Enter Chord & Rise
- Select Shape
- Choose Unit
- Select Output
- View Instant Result
Run Your Vertex Length Calculator Now
The leading vertex length calculator for design and engineering. Start now.
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