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Every measurement of a circle is tied to a single number — its radius. Give any one of the radius, diameter, circumference or area, and the other three follow directly from π.
Pick what you know, enter it, and get the complete set.
How is it calculated?
The four circle formulas
With r as the radius and π ≈ 3.14159:
| Quantity | Formula |
|---|---|
| Diameter (d) | 2 × r |
| Circumference (C) | 2 × π × r |
| Area (A) | π × r² |
| Radius from area | √(A ÷ π) |
Working backwards
Because each quantity depends only on the radius, the calculator first recovers the radius from whatever you entered — halving the diameter, dividing the circumference by 2π, or taking √(A ÷ π) from the area — then computes the rest.
Diameter vs radius — the common slip
The diameter is twice the radius, and mixing them up is the most frequent error. Area uses the radius squared, so using the diameter by mistake makes the area four times too big. Always confirm which one a problem gives you.
Where it helps
Geometry homework, working out the material for a round table or pizza, pipe and tank sizing, or the length of edging for a circular garden. For the volume of a sphere or cylinder, you need a 3-D formula, not the flat-circle area here.
Worked example
A circle has a radius of 5. Its diameter is 2 × 5 = 10, its circumference is 2 × π × 5 ≈ 31.42, and its area is π × 5² = 25π ≈ 78.54. Now suppose you only know the area is 78.54: the radius is √(78.54 ÷ π) = √25 = 5, and everything else follows — the calculator handles either direction.
FAQ
How do I find the area of a circle?+
Square the radius and multiply by π: A = π × r². A radius of 5 gives 25π ≈ 78.54. If you only have the diameter, halve it first.
How do I find the radius from the circumference?+
Divide the circumference by 2π: r = C ÷ (2π). A circumference of 31.42 gives a radius of about 5.
What is the difference between diameter and radius?+
The diameter is the full width across the circle through the centre; the radius is half of that. Diameter = 2 × radius.
How is circumference calculated?+
Circumference is 2 × π × radius, or equivalently π × diameter. For a radius of 5, that is 2π × 5 ≈ 31.42.
Can I start from the area?+
Yes. Choose "Area" as what you know; the calculator finds the radius with √(A ÷ π) and then the diameter and circumference.