Bow Front Calculator
Calculate the radius, chord length, sagitta (height), arc length, segment area and central angle for any curved bow front — ideal for furniture, cabinetry, and architectural design.
How the bow front calculator works
This calculator computes the complete geometry of a circular segment — the shape formed by a chord and an arc. Enter any two of the following: chord length (C), sagitta / height (H), or radius (R). The calculator will derive all remaining dimensions including arc length, central angle, and segment area.
Perfect for designing arched cabinets, curved countertops, bow-front furniture, window arches, and decorative architectural elements. The calculations are based on standard circle geometry relationships and are accurate to within 0.01 units.
Step 1: Dimensions
Bow Front Geometry
A bow front is a circular segment defined by a chord (C) and a sagitta (H). The radius (R) relates to these via: R = (C² / 8H) + (H / 2). Any two of these three values define the entire curve.
Step 2: Options
Design Tips
For furniture design, a typical bow front has a chord-to-height ratio between 6:1 and 10:1. Use the comparison table to visualise how different chord/height combinations affect the radius and arc length.
Bow Front Results
Calculated Radius
Chord / Height Variations
| Chord (C) | Height (H) | Radius (R) | Arc Length | Central Angle | Segment Area |
|---|
Geometry Visualisation
Key Formulas
Bow Front Geometry Equations
Radius: R = (C² / 8H) + (H / 2)
Central Angle (radians): θ = 2 × arcsin(C / 2R)
Arc Length: L = R × θ
Segment Area: A = (R² / 2) × (θ − sin θ)
Height from Radius & Chord: H = R − √(R² − (C/2)²)
Frequently Asked Questions
What is a bow front?
A bow front is a curved or arched front panel commonly used in furniture, cabinets, and architectural design. It creates a gentle convex curve that adds visual interest and dimension to the piece.
How do you calculate the radius of a bow front?
Given the chord length (C) and sagitta (height, H), the radius R is calculated using the formula: R = (C² / 8H) + (H / 2). This is derived from the circle geometry relationship between chord, sagitta and radius.
What is the sagitta of a bow front?
The sagitta is the height or depth of the curve — the maximum distance from the chord (straight line between the two endpoints) to the arc. It represents how ‘deep’ the bow is.
How is arc length calculated for a bow front?
Arc length is calculated using the formula: Arc Length = Radius × Central Angle (in radians). The central angle is computed from the chord and radius using the inverse sine function.
What is the segment area of a bow front?
The segment area is the area enclosed by the chord and the arc. It is calculated using the formula: Segment Area = (R² / 2) × (θ − sin θ), where θ is the central angle in radians.
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