Equação do Círculo
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
(x−h)²+(y−k)²=r²
About this calculator
The circle equation calculator allows you to determine the reduced equation of a circle from its center and radius, or to find the center and radius from a given equation. It uses the formula (x−h)²+(y−k)²=r², where (h,k) is the center and r is the radius. The tool can also complete squares to convert general equations into the reduced form.
This calculator is useful for analytic geometry students, engineers, and professionals who need to solve problems involving circles, such as determining the position of a point relative to a circle, calculating distances between centers, or checking whether an equation represents a circle. It speeds up calculations that would be tedious to do manually.
When using the calculator, ensure you enter the center and radius values correctly, or the general equation. Remember that the radius must be a positive number. If the general equation does not represent a circle (for example, a negative radius), the tool will indicate an error. Also check that the coefficients are in standard form before using the square completion feature.
Frequently asked questions
How can I find the center and radius of a circle from its general equation?
Enter the general equation into the calculator and it will use the method of completing the square to find the center and radius automatically.
What does it mean if the calculated radius is negative?
If the radius is negative, the equation does not represent a real circle, as the radius must be positive. Check the entered coefficients.
Can I use this calculator for circles with center not at the origin?
Yes, the calculator accepts any center (h,k), not just the origin. Simply enter the correct values of h, k, and r.
Can the calculator handle equations that are not in reduced form?
Yes, it can process general equations of the form x²+y²+Dx+Ey+F=0 and convert them to reduced form, provided they represent a circle.