Radius of Circle from Chord Length and Arc Height

vCalc Reviewed

r = \frac{{(L)}^{2}}{8 \cdot h} + \frac{h}{2}

$r = ( L )^2 / (8* "h" ) + "h" /2$

(L) Length of Chord

$(L) "Length of Chord"$

(h) Height of Arc

$(h)"Height of Arc"$

The Math / Science

The formula for the radius of a circle based on the length of a chord and the height is:

$r = \frac{L^{2}}{8 h} + \frac{h}{2}$ $r = L^2/(8 h) + h/2$

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.

Circle Calculators

Circle Area - Computes the area of a circle given the radius (A = π r²).
Area of Circle Arc Segment f(r,θ) - Computes the area of an arc segment of a circle given the radius (r) and angle (θ)
Area of Circle Arc Segment Area f(r,h) - Computes the area of an arc segment of a circle given radius (r) and the depth (h) into the circle.
Area of Circle Sector f(r,Θ) - Computes the area of a sector (pie slice) of a circle given the radius (r) and angle (Θ).
Angle of Circle Sector f(r,h) - Computes the angle in a circle from the radius and depth of the chord.
Area of Circle Annulus - Computes the area of an annulus (ring) given the inner radius (r) and outer radius (R).
Radius of Circle from Center and a Point - Computes the radius of a circle given the center point (h,k) and any other point (x,y) on the circle.
Circumference of Circle - Computes the circumference of a circle given the radius (C = 2 π r).
Circle Arc Length - Computes the length of an arc length on a circle given the radius (r) and angle (Θ)
Circle within a Triangle - Computes the radius of a circle inscribed within a triangle given the length of the three sides (a,b,c) of the triangle.
Circle around a Triangle - Computes the radius of a circle that circumscribes a triangle given the length of the three sides (a,b,c) of the triangle.
Circle Diameter from Area - Computes the radius and diameter of a circle from the area.
Circle Radius from Circumference - Computes the radius of a circle given the circumference.
Circle Circumference from Area - Computes the circumference of a circle given the area.
Circle Radius from Area - Computes the radius of a circle given the area.
Chord Length: Computes the length of a chord in a circle from the radius and height.
Chord Length from Arc Length and Radius: Computes the length of a chord on a circle based on the circle's radius (r) and the length of the arc (a).
Circle Radius from Chord - Computes the radius of a circle based on the length of a chord and the chord's center height.
Circle Equation from Center and one Point - Develops the general equation of a circle based on the coordinates of the center (h,k) and any point on the circle (x,y).
Circle Equation from Three Points: Develops the general equation of a circle that goes through three points that are not in a straight line.
Circle with same Perimeter as an Ellipse - Computes the radius of the circle with the same perimeter of an ellipse defined by the semi-major and semi-minor axes.
Rectangles to Cover a Circle - Computes the number of rectangles needed to minimally cover a circle based on the circle's diameter and the length and width of the rectangles.