Circles in simple words
A circle has four main measurements. The radius is the distance from the center to the edge. The diameter is the distance all the way across through the center, which is two radii. The circumference is the distance around the circle. The area is the flat space inside it.
They are all linked by the number π (pi), which is about 3.14159. Going around a circle is always a little more than 3 times as long as going across it.
Example: a circle with a radius of 5 cm has a diameter of 2 × 5 = 10 cm, a circumference of 2 × π × 5 ≈ 31.42 cm and an area of π × 5 × 5 ≈ 78.54 cm².
Enter any one of the four measurements and the calculator finds the other three, showing each step with your number.
Formula and method
The circle identities are d = 2r, C = 2πr and A = πr². Recover the radius from diameter by dividing by 2, circumference by dividing by 2π, or area by taking √(A/π). All other measurements follow from that radius.
Worked example
A circle of radius 5 m has diameter 10 m, circumference 31.41592654 m and area 78.53981634 m². An area of 100π m² instead gives radius 10 m.
Inputs and limitations
Choose an area unit when the known measurement is area. Results use meters and square meters unless you choose another output unit. A diameter used as a radius doubles circumference and quadruples area; check which measurement you have before calculating.
Answers in terms of π
When the radius is a clean number, the calculator also writes the circumference and area as multiples of π. For r = 2, C = 2π × 2 = 4π and A = π × 2² = 4π, so both happen to equal about 12.566. Exact π forms are what most geometry courses expect as final answers.
The steps start from whichever value you entered: r = d ÷ 2, r = C ÷ 2π or r = √(A ÷ π), then substitute that radius into each formula.