How to use the circle equation from three points calculator
Find the circle through three points. Enter x₁, y₁, x₂, y₂, x₃, y₃ in the fields above; the center x, center y, radius are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- x1 — x₁
- y1 — y₁
- x2 — x₂
- y2 — y₂
- x3 — x₃
- y3 — y₃
Worked example
With x₁ = 0, y₁ = 0, x₂ = 4, y₂ = 0, x₃ = 0, y₃ = 3, the calculator gives center x ≈ 2; center y ≈ 1.5; radius ≈ 2.5.
Frequently asked questions
What is the formula for the circle equation from three points calculation?
Center x = ((x1 × x1+y1 × y1) × (y2-y3)+(x2 × x2+y2 × y2) × (y3-y1)+(x3 × x3+y3 × y3) × (y1-y2)) / (2 × (x1 × (y2-y3)+x2 × (y3-y1)+x3 × (y1-y2))). Center y = ((x1 × x1+y1 × y1) × (x3-x2)+(x2 × x2+y2 × y2) × (x1-x3)+(x3 × x3+y3 × y3) × (x2-x1)) / (2 × (x1 × (y2-y3)+x2 × (y3-y1)+x3 × (y1-y2))). Radius = hypot(x1-[Center x],y1-[Center y]). Here x1 is x₁, y1 is y₁, x2 is x₂, y2 is y₂, x3 is x₃, y3 is y₃.
What inputs do I need for the circle equation from three points calculator?
You need x₁, y₁, x₂, y₂, x₃, y₃. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.