The Radius of a Circle based on the Chord and Arc Height calculator computes the radius based on the chord length (L) and height (h).
INSTRUCTIONS: Choose units and enter the following:
- (L) Length of Chord (see diagram)
- (h) Height of Arc from the chord to the highest point.
Radius (r): The calculator returns the radius in meters. However, this can be automatically converted to compatible units via the pull-down menu.
The Math / Science
The formula for the radius of a circle based on the length of a chord and the height is:
`r = L^2/(8 h) + h/2`
where:
- r is the radius of a circle
- L is the length of the chord. This is the straight line length connecting any two points on a circle.
- h is the height above the chord. This is the greatest distance from a point on the circle and the chord line.
A useful application of the math construct is in construction where the formulas computes the radius of an arch.
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