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Circle Equation Calculator.

Generate the standard equation of a circle from center and radius.

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Set your values

Results update as you type.

Standard equation: (x - 2)² + (y + 1)² = 16

Standard equation

(x - 2)² + (y + 1)² = 16

Results update automatically as you type.

Use Cases

Graphing a Circle

Quickly convert center and radius into the standard equation, which is useful for graphing the circle on a coordinate plane or for further analysis.

Example: For center (2, -3) and radius 5, the equation is (x - 2)^2 + (y + 3)^2 = 25.

Solving Geometry Problems

When you know the center and radius of a circle, this calculator helps you write its equation, which is often required in math homework or tests.

Example: Find the equation of a circle with center (0, 0) and radius 1: x^2 + y^2 = 1.

Frequently Asked Questions

What does the Circle Equation Calculator do?
It takes the center coordinates (h, k) and the radius (r) of a circle, then outputs the standard equation of that circle: (x - h)^2 + (y - k)^2 = r^2. You input the values, and it generates the equation for you.
How do I use the Circle Equation Calculator?
Enter the x-coordinate of the center in the 'Center h' field, the y-coordinate in the 'Center k' field, and the radius in the 'Radius' field (in units). The calculator will then display the standard equation of the circle.
What is the standard equation of a circle?
The standard equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. This equation represents all points (x, y) that are exactly r units away from the center.

Tips & Common Mistakes

Tips

  • Ensure the radius is a positive number; if you enter a negative value, the calculator may still work but the radius should be positive in standard form.
  • Double-check the signs: if the center has a negative coordinate, the equation will have a plus sign because of the minus in (x - h). For example, center (2, -3) gives (x - 2)^2 + (y + 3)^2.
  • Use the same units for all inputs; the radius is in units, and the center coordinates are in the same coordinate system.
  • If you need the general form, you can expand the standard equation, but this calculator provides the standard form directly.

Common Mistakes to Avoid

  • Forgetting to square the radius: the equation uses r^2, not r. For radius 5, the right side is 25, not 5.
  • Misplacing signs: if the center is (h, k), the equation has (x - h) and (y - k). If h or k is negative, the sign becomes positive in the equation.
  • Entering the radius as the diameter: the radius is half the diameter, so make sure you input the correct value.

Last updated: August 13, 2026