Substituting the coordinates of the center and radius we get, Squaring both sides of the equation, yields the standard equation of a circle:įind the equation of the circle with center (4, -3) and radius 5. Given a circle with radius, r, centered at point (h, k), we can use the distance formula to find that The standard equation of a circle is derived using the distance formula. Derivation of the standard equation of a circle This equation can be used for a circle that lies anywhere in the coordinate plane. The standard equation of a circle is (x - h) 2 + (y - k) 2 = r 2. In coordinate geometry, a circle can be expressed using different equations and based on various constraints. Where C is the circumference and π is a mathematical constant approximately equal to 3.14159. Where d is the diameter and π is a mathematical constant approximately equal to 3.14159. Where r is the circle's radius and π is a mathematical constant approximately equal to 3.14159. The figure below depicts the area of a circle in red bounded by the circumference in grey. The area of a circle is the plane region bounded by the circle's circumference. The area of a circle formula is A = πr 2. The arc length, s, of a circle is, where θ is the central angle, as shown in the figure below. Where A is area and π is a mathematical constant approximately equal to 3.14159. There are a few circumference of a circle formulas. Imagine cutting the circle and straightening it out the length of the straightened line is the circumference. Circumference is a measure of the distance around the circle. ![]() The circumference of a circle is C = 2πr. The diameter of a circle, is d = 2r, where d is the diameter and r is the radius: The figure below shows the key parts of a circle that we need to know to be able to work with circles and their formulas. There are many circle formulas, such as the area of a circle formula, circumference formula, and diameter formula, all of which are discussed below along with the equations for a circle. Home / geometry / circle / circle formula Circle formulaĪ circle is defined as the set of all points equidistant from a fixed point on a plane.
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