Chord to Radius Calculator

Last updated: 06 Oct 2025 | Author: Brij | Review By: Irshad

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Quickly calculate the radius of a circle from chord length and arc height using our free Chord to Radius Calculator. Ideal for architects, engineers, and DIY projects.

Chord Length:

Arc Height / Sagitta:

Height from chord midpoint to arc

Circle Radius Calculation Results

Circle Radius:

In geometry and construction, you often need to calculate the radius of a circle when you know the chord length and the arc height (sagitta). The Chord to Radius Calculator makes this quick and easy, helping with designs, arches, and circular layouts.

Formula

Formula to Calculate Radius from Chord and Sagitta

$R = \frac{C^2}{8H} + \frac{H}{2}$

This formula comes from the geometry of a circle and allows you to determine the radius using just the chord length and arc height.

Example

Suppose you have:

Chord Length (C) = 20 ft
Arc Height / Sagitta (H) = 2 ft

Using the formula:

$R = \frac{20^2}{8 \times 2} + \frac{2}{2} = \frac{400}{16} + 1 = 25 + 1 = 26 \text{ ft}$

So, the circle radius = 26 ft.

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