Equation of a Circle Calculator

Standard Form
General Form
Area
Circumference

How It Works

This equation of a circle calculator uses established formulas to provide accurate results.

The basic rule:

  • (x - h)² + (y - k)² = r²
  • x² + y² + Dx + Ey + F = 0
  • Area = πr²
  • Circumference = 2πr

Results are estimates. Consult a professional for critical decisions.

Want to Actually Learn Algebra?

Calculators give you answers — but if you want to understand the math, Allday Everyday Math teaches Algebra 1 fast with structured lessons, worked examples, and practice quizzes that build real confidence.

Explore Allday Everyday Math →

Frequently Asked Questions

What is the standard form of a circle equation?

The standard form is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. This form clearly shows the center and radius.

What is the general form of a circle equation?

The general form is x² + y² + Dx + Ey + F = 0, where D = -2h, E = -2k, and F = h² + k² - r². To convert back to standard form, complete the square.

How do I find the center and radius from general form?

Given x² + y² + Dx + Ey + F = 0, the center is (-D/2, -E/2) and the radius is √((D/2)² + (E/2)² - F). Use the Circle Properties from Equation calculator for this.

What if the center is at the origin?

When the center is (0, 0), the equation simplifies to x² + y² = r². This is the simplest form of a circle equation.