Circle Calculator: Area, Circumference, Diameter, and Equation
Calculate every main measurement of a circle (radius, diameter, circumference, area) plus the standard and general form equations starting from any single known input.
Provide exactly one measurement (radius, diameter, circumference, or area). Leave the other measurement fields empty so the engine can derive the radius and update the remaining values.
Supply the center coordinates and equation radius to render both analytic forms.
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How to use
Enter exactly one of the circle measurement fields (radius, diameter, circumference, or area). Leave the others empty so the calculator can derive the radius and update every dependent value automatically.
Use the circle equation inputs (center h, center k, and radius) to display the standard form $(x-h)^2 + (y-k)^2 = r^2$ and its general form $x^2 + y^2 + Dx + Ey + F = 0$.
Methodology
The engine resolves the supplied measurement into the canonical radius, then recalculates diameter, circumference, and area with deterministic rounding so the interface never shows NaN or Infinity.
- Diameter inputs derive the radius by halving the value; circumference inputs divide by $2\pi$; area inputs use $\sqrt{A/\pi}$.
- Output values (radius, diameter, circumference, area) are rounded consistently to six decimal places for parity across browsers.
- The equation builder reuses the provided equation radius and center coordinates for both the standard and general forms.
Full original guide (expanded)
Essential circle formulas and audit notes from the legacy page remain here to preserve contextual guidance.
0.1.0-draft · 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido · LinkedIn