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Geometry Precision
Circle Calculator (Radius, Area, Circumference)
Compute any property of a circle instantly. Enter radius, diameter, circumference, or area to solve all other dimensions with exact π and rounded decimal values.
Interactive Multi-Variable Circle Solver
π ≈ 3.1415926535
units
units
units
units²
Radius (r)
5.0000
Diameter (d)
10.0000
Circumference (C)
31.4159
Area (A)
78.5398
Geometric Properties of a Circle: Fundamental Formulas
A circle is defined in Euclidean plane geometry as the set of all points that are an equal distance (known as the radius) from a central point. Circles are among the most symmetrical and mathematically elegant shapes in existence.
Core Geometric Circle Equations
Diameter: d = 2r
Circumference: C = 2πr = πd
Area: A = πr² = π(d/2)² = C² / (4π)
Reverse Calculations & Derivations
- Solving for Radius from Area: If the area $A$ is known, divide by $pi$ and take the square root: $r = sqrt{A / pi}$.
- Solving for Radius from Circumference: If the circumference $C$ is known, divide by $2pi$: $r = C / (2pi)$.
- Finding Circumference from Area: $C = 2sqrt{pi A}$.
| Radius (r) | Diameter (d) | Circumference (C) | Area (A) |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 3 | 6 | 18.8496 | 28.2743 |
| 5 | 10 | 31.4159 | 78.5398 |
| 10 | 20 | 62.8319 | 314.1593 |
| 15 | 30 | 94.2478 | 706.8583 |
Frequently Asked Questions
Pi (π) is an irrational mathematical constant representing the ratio of a circle's circumference to its diameter. Its decimal representation is non-terminating and non-repeating: 3.141592653589793... The fraction 22/7 is commonly used as an approximation.
If you know the diameter, use $A = pi (d/2)^2$. If you only know circumference, use $A = C^2 / (4pi)$.
Educational Disclaimer: Local JavaScript math execution uses IEEE-754 double precision standard.