Calculate circle radius, diameter, circumference, and area from any one known value with US & Metric unit conversions and exact multiples of π.
• Select your preferred US unit (inches, feet, yards, miles) or Metric unit (mm, cm, meters, km) in the numerical value section.
• Provide any ONE value (Radius, Diameter, Circumference, or Area). The tool automatically computes all 3 other properties.
Please provide any value below to calculate the remaining values of a circle.
Select your unit and enter any one value on the left to compute the remaining circle dimensions.
Fundamental circle properties, exact mathematical derivations, and geometric theorems.
In Euclidean geometry, a circle is the locus of all points in a 2D plane that are at a fixed distance (the radius, $r$) from a given center point. The ratio of any circle's circumference to its diameter is the invariant mathematical constant π (pi ≈ 3.14159265...).
| Given Parameter | Radius (R) | Diameter (D) | Circumference (C) | Area (A) |
|---|---|---|---|---|
| Radius (R) | — | 2R | 2πR | πR² |
| Diameter (D) | D / 2 | — | πD | π(D/2)² |
| Circumference (C) | C / (2π) | C / π | — | C² / (4π) |
| Area (A) | √(A / π) | 2√(A / π) | 2√(πA) | — |
All linear circular formulas remain identical regardless of unit system: Diameter is always 2 × radius, and Circumference is 2π × radius (e.g. 5 feet radius = 10 feet diameter = 31.42 feet circumference).
One acre is exactly equal to 43,560 square feet. To convert circular area from square feet to acres, divide the calculated area in ft² by 43,560.
Because area is proportional to the square of the radius (A = πr²). When the radius is multiplied by 2, the area becomes π(2r)² = 4πr², which is 4 times larger.
In analytical geometry, expressing answers as multiples of π (such as C = 10π or A = 25π) provides exact values without decimal rounding error.