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Math

Circle Calculator (radius / diameter / circumference / area)

Pick which value you know — radius r, diameter d, circumference C or area A — type the number, and the calculator returns the other three plus the inscribed-square side (largest square inside the circle) and the bounding-square side (smallest square that contains it). Lengths share one unit and area uses that unit squared. Useful for design, engineering, DIY and geometry homework.

Radius r

10

Given

Diameter d

20

Computed

Circumference C

62.8319

Computed

Area A

314.1593

Computed

Inscribed square side

14.1421

Largest square that fits inside the circle (side = r √2).

Bounding square side

20

Smallest square that contains the circle (side = d).

Formula

d = 2r ; C = 2πr = πd ; A = πr²

Units are up to you (cm, m, in, ft, km — all fine). Lengths share one unit; area uses that unit squared. π ≈ 3.14159265358979.

Formula

d = 2 r ; C = 2 π r = π d ; A = π r²

Frequently asked

Why aren’t circumference and area whole numbers?

Because the formulas contain π (≈ 3.14159265…), which is irrational — it can never be expressed as a ratio of two integers. So unless you pick a contrived radius like 1/π, integer inputs almost always yield non-integer circumference and area. The result is displayed to 4 decimal places, which is more than enough for most design and DIY work — round it off when you actually cut or measure.

Which grows faster — circumference or area — as the radius increases?

Area (A = π r²) grows with the square of the radius, so it grows much faster. Double the radius and the circumference doubles (×2) while the area quadruples (×4); triple it and circumference ×3 but area ×9. That’s why one 12-inch pizza is bigger than two 6-inch pizzas put together — 6 + 6 ≠ 12 in pizza-area terms (twice the diameter is four times the area).

What are the inscribed and bounding squares actually used for?

Both come up in real work. The bounding square (= diameter) is the smallest square sheet of material — fabric, paper, metal — that can fully cover the circle, so it’s what you order when fabricating a round mirror, cake board, or disc. The inscribed square (= r √2) is the largest square that fits inside the circle, so it tells you the biggest square peg that can pass through a round hole — useful when threading square stock through a circular pipe, or when fitting a square photo inside a round frame.

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