# Circle - Equation

### Unit Circle

The equation of a unit circle - where the center of the circle is located in the origo of the coordinate system and the *radius = 1* - can be expressed as

*x ^{2} + y^{2} = 1 (1)*

### Standard Form

The standard form for the equation of a circle can be expressed as

*(x - a) ^{2} + (y - b)^{2} = r^{2} (2)*

*where *

*a = x coordinate position of the circle center*

*b = y coordinate position of the circle center*

*r = circle radius*

### General Form

The general form for the equation of a circle can be expressed as

*x ^{2} + y^{2} + A x + B y + C = 0 (3)*

*where *

*A, B, C = constants*

### Radius of circle

* r = (a ^{2} + b^{2} - C) ^{1/2} (4)*

### Coordinates in the Circle Centre

*a = - A / 2 (5a)*

*b = - B / 2 (5b)*

## Related Topics

### • Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

## Related Documents

### Area of Intersecting Circles

Calculate area of intersecting circles

### Cartesian Coordinate System - Distance and Intermediate Position Between Two Points

Distance and intermediate position between two point in a cartesian x and y coordinate system.

### Centroids of Plane Areas

The controid of square, rectangle, circle, semi-circle and right-angled triangle.

### Circle - the Chord Lengths when Divided in to Equal Segments

Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.

### Circles - Circumferences and Areas

Circumferences and areas of circles with diameters in inches.

### Distance between 3D Points

Distance between two points in a three dimension x, y and z coordinate system - online calculator.

### Elementary Curves

Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines.

### Equal Areas - Circles vs. Squares

Radius and side lengths of equal areas, circles and squares.

### Geometric Shapes - Areas

Areas, diagonals and more - of geometric figures like rectangles, triangles, trapezoids ..

### Polar vs. Cartesian Coordinates

Convert between Cartesian and Polar coordinates.

### Radians vs. Degrees

Radian is the SI unit of angle. Convert between degrees and radians. Calculate angular velocity.

### Smaller Circles within a Large Circle - Calculator

Calculate the number of small circles that fits into an outer larger circle - ex. how many pipes or wires fits into a larger pipe or conduit.

### Smaller Rectangles within a Larger Rectangle

The maximum number of smaller rectangles - or squares - within a larger rectangle (or square).