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.
Enter a positive number.
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
- · π uses JavaScript’s built-in Math.PI ≈ 3.141592653589793 — no early rounding.
- · Units are yours to choose. If r is in cm, then d and C are in cm and A is in cm². Switching to inches gives in² etc.
- · Inscribed square side = r √2 ≈ 1.4142 r — the largest square that fits inside, touching the circle at all four corners.
- · Bounding square side = d = 2 r — the smallest square that fully contains the circle (handy for cutting stock or packaging).
- · Only the 2-D circle is computed here. Sphere volume (4/3 π r³) and cylinder volume are separate tools.
- · Sources: Euclid, Elements, Book III (geometry of circles); CRC Standard Mathematical Tables and Formulae, 31st ed., §4.6 “Circles” (Zwillinger, 2003).
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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