About

In architecture, machining, and woodworking, creating a perfect arch often requires calculating the 'Sagitta'—the vertical height from the center of the chord to the highest point of the arc. Whether you are bending a pipe, designing a window, or laying out a bridge, knowing this dimension is critical for structural integrity and aesthetics.

This tool eliminates the guesswork. By inputting the Chord Length (the width of the base) and the Radius of the circle, it instantly computes the Sagitta. It also generates a visual blueprint diagram, complete with dimension lines, to help you visualize the geometry before you cut or build.

Formulas

The Sagitta is calculated using the Pythagorean theorem applied to the triangle formed by the radius, half the chord, and the apothem:

s = R - √R² - (L2)²

Reference Data

Variable	Symbol	Description
Radius	R	Distance from circle center to edge.
Chord	L	Straight line distance between arc endpoints.
Sagitta	s	Height of the arc from the chord midpoint.
Apothem	d	Distance from center to chord (R - s).

Frequently Asked Questions

This is geometrically impossible. The chord length cannot exceed twice the radius (Diameter). The tool will alert you if your inputs violate this rule.

Yes, the formula can be rearranged: R = (s² + (L/2)²) / (2s). This is useful when measuring an existing arch to find the radius needed to replicate it.

Sagitta is Latin for 'arrow'. In geometry, it resembles an arrow resting on the bowstring (the chord).

Absolutely. CNC machines often require arc parameters defined by start point, end point, and radius. Calculating the sagitta verifies that the programmed arc clears obstacles or fits within stock material.