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.
Common searches this calculator answers include “circumcircle”, “circle through points”, “center and radius”, “calculate circle equation from three points”, “find center x”.
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 circle equation from three points calculator used for?
Find the circle through three points. It helps with questions such as “circumcircle”, “circle through points”, “center and radius”.
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 the circle equation from three points 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 circle equation from three points 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.