Equation of a Circle Calculator
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.
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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.