Radius of Circle from Chord Length and Arc Height

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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