How this calculator works
Every measurement of a circle — radius, diameter, circumference, and area — can be derived from any one of the others, because all four are tied together by π. Enter whichever value you already know and this calculator works out the rest.
Internally, the calculator always solves for the radius first, since it is the simplest starting point, then derives the diameter, circumference, and area from it. That means the same underlying circle comes out identically no matter which of the four values you started from.
How do you calculate the circumference and area of a circle?
Diameter: d = 2rCircumference: C = 2πr = πdArea: A = πr²Solving backward: r = d ÷ 2 = C ÷ (2π) = √(A ÷ π)Worked example: starting from a circumference of 2π
- Solve for radius: r = C ÷ (2π) = 2π ÷ (2π) = 1.
- Diameter: d = 2 × 1 = 2.
- Area: A = π × 1² = π ≈ 3.1416.
- This is the unit circle: radius 1, diameter 2, circumference 2π, area π.
Frequently asked questions
What is the difference between radius and diameter?
The radius is the distance from the center of the circle to its edge; the diameter is the full distance across the circle through the center, which is always exactly twice the radius.
Why does circumference use π and not diameter directly?
π is defined as the ratio of a circle's circumference to its diameter (C ÷ d), which is true for every circle regardless of size. That is exactly why C = πd (equivalently 2πr) works universally.
How do I get radius from area?
Rearrange A = πr² to solve for r: divide the area by π, then take the square root, giving r = √(A ÷ π). This calculator does that step automatically in area mode.
Does it matter which value I start with?
No. Because radius, diameter, circumference, and area are all mathematically tied together, starting from any one of them and solving for the others always describes the same circle.
How do I find the area of a half-circle (semicircle)?
Take half of the full-circle area formula: semicircle area = (π × r²) ÷ 2. For a radius of 5, the full circle's area is π × 5² = 25π ≈ 78.54, so the semicircle's area is half that, 12.5π ≈ 39.27.