An online calculator and solver to find the center and radius of a circle given its
equation in the form
Complete the Square to Find the Center and Radius
The calculator uses the following idea: completes the squares as follows
x 2 + a x = (x + a/2)
2 - (a/2) 2
and
y 2 + a y = (y + b/2)
2 - (b/2) 2
Substitute the above into the original equation and write in the
standard form of the equation of a circle
(x -
h) 2 + (y - k)
2 = r 2
such that the center has coordinates (h , k) = (-a/2 , -b/2) and radius
r such that r 2 = c + (a/2)
2 + (b/2) 2
How to Use the Calculator?
1 - Enter the coefficients a, b, c and the number of decimal places desired as real number and press "enter". If the given equation is that of a circle, it will give an answer: the x and y coordinates of the center and the radius.
More References and links
Equation of a Circle .
Tutorial on Equation of Circle with
solutions
Maths Calculators and Solvers .
Welcome to the center of a circle calculator that finds the center of a circle for you. Here, we'll show you how to calculate the center of a circle from the various circle equations. We'll also cover finding the center of a circle without any math!
How do I use the center of a circle calculator?
The center of a circle calculator is easy to use.
- Select the circle equation for which you have the values.
- Fill in the known values of the selected equation.
- You can find the center of the circle at the bottom.
Read on if you want to learn some formulas for the center of a circle!
How do I calculate the center of a circle?
Circles can be defined with multiple equations. If you have a mathematical formula for your circle, pick the correct one from the headings below. We'll then explain how to calculate the center of the circle from there.
The standard equation of a circle
The standard equation of a circle is:
(x−A)2+(y−B)2=C\small (x - A)^2 + (y - B)^2 = C
where C=r2C = r^2, or the radius squared.
With this equation, we can find the center of the circle at point (A,B)(A, B). Be careful of the signs!
The parametric equation of a circle
The parametric equation of a circle is defined as:
x=A+r ⋅ cos(α)y=B+r ⋅ sin(α)\small \begin{split} x &= A + r\!\cdot\!\cos{(\alpha)} \\ y &= B + r\!\cdot\!\sin{(\alpha)} \end{split}
In this form, we can calculate the center of the circle as (A,B)(A,B) again.
The general equation of a circle
A less common circle equation is the general equation of a circle:
x2+y2+D ⋅ x+E ⋅ y+F=0\small x^2 + y^2 + D\!\cdot\!x + E\!\cdot\!y + F = 0
In the general equation, we can calculate the center of the circle as (−D2,− E2)\left(-\frac{D}{2}, -\frac{E}{2}\right).
How do I find the center of a physical circle?
If you have a circle drawn on paper, there's no center of a circle formula. Instead, follow these steps:
- Draw two (or more) chords on the circle.
- Find these chords' midpoints.
- From the midpoints, draw lines that are perpendicular to the chords.
- The point where these lines intersect is the circle's center.
- Congrats, you can find the center of the circle!
FAQ
What is the center of a circle represented by the equation (x+9)² + (y−6)² = 10²?
The center of this circle is (−9, 6), with a radius of 10. The equation (x+9)² + (y−6)² = 10² is in the standard circle equation form (x−A)² + (y−B)² = C, making A = −9 and B = 6.
What is the center of a circle represented by the equation (x−5)² + (y+6)² = 4²?
The center of this circle is (5, −6), with a radius of 4. The equation (x−5)² + (y+6)² = 4² is in the standard circle equation form (x−A)² + (y−B)² = C, making A = 5 and B = −6.
What is the center of a circle given the equation (x−5)² + (y+7)² = 81?
The center of this circle is (5, −7), with a radius of √81 = 9. The equation (x−5)² + (y+7)² = 81 is in the standard circle equation form (x−A)² + (y−B)² = C, making A = 5 and B = −7.