Circle Calculator: Area, Circumference, Diameter, Radius
This calculator can solve for the four main properties of a circle. Enter a value for **any one** of the properties below (Radius, Diameter, Circumference, or Area), and the tool will instantly derive all the others.
Geometric Properties
Results
Radius ($r$)
Diameter ($d$)
Circumference ($C$)
Area ($A$)
Step-by-Step Derivation
Circle Equation Calculator
Find the standard form of the circle equation, $(x - h)^2 + (y - k)^2 = r^2$, given the center and radius.
Standard Form: $(x - h)^2 + (y - k)^2 = r^2$
Standard Equation
General Form
Geometric Formulas for Circle Properties
The entire geometry of a circle can be calculated if the radius ($r$) is known. The relationships are defined by the constant $\pi \approx 3.14159$ .
| Property | Formula (using $r$) | Inverse Formula (to find $r$) |
|---|---|---|
| Diameter ($d$) | $d = 2r$ | $r = d/2$ |
| Circumference ($C$) | $C = 2\pi r$ | $$r = \frac{C}{2\pi}$$ |
| Area ($A$) | $A = \pi r^2$ | $$r = \sqrt{\frac{A}{\pi}}$$ |
Circle Equations (Analytic Geometry)
In a coordinate plane, the location and size of a circle are described by its equation. The circle is defined as the set of all points $(x, y)$ that are equidistant (distance $r$) from a fixed center point $(h, k)$.
Standard Form (Center-Radius Form)
This is the simplest form, directly showing the center $(h, k)$ and the radius $r$:
General Form
The general form is found by expanding the standard form:
Where the center coordinates are related by $h = -D/2$ and $k = -E/2$.
Frequently Asked Questions (FAQ)
What is the formula for the Area of a Circle?
What is the formula for the Circumference of a Circle?
What is the standard form equation of a circle?
What is the relationship between the circle and the ellipse?
Formula (LaTeX) + variables + units
','
r = \frac{C}{2\pi}
r = \sqrt{\frac{A}{\pi}}
(x - h)^2 + (y - k)^2 = r^2
x^2 + y^2 + Dx + Ey + F = 0
{std_eq_h}^2 + ${std_eq_k}^2 = ${formatNumber(r_sq)}
$(x - h)^2 + (y - k)^2 = r^2$
$x^2 + y^2 + Dx + Ey + F = 0$
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 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.