The Circle from Three Points calculator computes center points and radius of a circle defined by three points not in a straight line.
INSTRUCTIONS: Enter the following:
- (P1) X and Y coordinates of Point 1
- (P1) X and Y coordinates of Point 2
- (P2) X and Y coordinates of Point 3
Circle from Three Points (CP): The calculator returns the center point and the radius as real number.
The Math / Science
The Circle from Three Points equation computes the center point and radius of a circle. It does this by solving the general form of the equation of a circle (below) for the three coefficients (g, f and c). With g, f and c, one can then solve for the center points (h, k) and radius (r) as follows:
h = -1*g
k = -1*f
`r = sqrt(h * h + k * k - c)`
The general form of the equation of a circle is:
x2 + y2 + 2gx + 2fy + c = 0
The common form of the equation of a circle, employing the radius and center points is:
r2 = (x-h)2 + (y-k)2
where:
- (h, k) is the center of the circle
- r is the radius
Circle Calculators
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- 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.