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Step #1

Enter the the 3 Known Points of the circle into X1, Y1, X2, Y2, X3 and Y3

Step #3

Find the Slopes:

Slope 1:

Slope1= (X1 -

Slope 2:

Slope2= (X1 -

Step #4

Find the Perpendiculars:

Perpendicular 1:

Perp1= YMid1 -

Perpendicular 2:

Perp2= YMid2 -

Step #5

Calculate the X,Y Center Points of the Circle

X Center Point = (Perp1 -

Y Center Point = Perp1 + (Slope1 x XCenter)

How to Find the Center Point of a Circle When 3 Points are Known

Step #2

Find the Mid Point of each chord of the circle:

Find X Midpoints:

XMid1= (X1 + X2) / 2

XMid2= (X1 + X3) / 2

Find Y Midpoints:

YMid1= (Y1 + Y2) / 2

YMid2= (Y1 + Y3) / 2

Step #6 (Optional)

Calculate the Circle Radius

Circle Radius = Square Root of ((X Center -

As you can see, the calculations for determining the center point and radius of a circle using 3 known points can be a cumbersome process. Fortunately there is a much faster and easier way. The Web Machinist Circle Center 3 Points Calculator included in the Web Machinist Software Program. (See below):

The Circle Center 3 Points Calculator above is Available as Part of the Web Machinist Software Program that you can Purchase Here

Above is the Circle Center Dialog where all you need to do is enter 3 known points on the circle then the Circle Center 3 Points Calculator will determine the circle center and the circle radius quickly and easily. See Below:

Web Machinist Software:

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