What is the area of a circle with radius 12?

The area is 144π, which is 452.389342 square units. The formula is A = πr², so squaring the radius gives 12 × 12 = 144, and multiplying by π gives 452.389342. Because the radius squares, the area of this circle is 144 times that of the unit circle rather than 12 times.

What is the circumference of a circle with radius 12?

The circumference is 24π, or 75.398224 units. It comes from C = 2πr, so 2 × 12 = 24, then × π. The same circle has a diameter of 24, and since C = πd you can get there either way — 24π is the same as 24π. Dividing the circumference by the diameter returns π itself, 3.14159265, which is true for every circle and is where the constant comes from.

How much bigger is radius 12 than radius 11?

The radius goes up by 9.09%, from 11 to 12, but the area goes up by 19.01% — from 380.132711 to 452.389342. That is the square law: the area ratio is (12/11)² = 1.190083. The circumference, being linear, rises by the same 9.09% as the radius.

What fits inside a circle of radius 12?

A square inscribed in it has a diagonal equal to the diameter, 24, so its side is 12√2 = 16.970563 and its area is 2r² = 288 — about 63.7% of the circle, a proportion that is the same for every circle. A regular hexagon inscribed in it has a side of exactly 12, since the hexagon side always equals the radius, giving a perimeter of 72 against a circumference of 75.398224.

Can a circle’s area ever be a whole number?

Only if the radius is irrational in the right way. Since A = πr², getting a whole number area requires r² to be a whole number divided by π, and π is transcendental, so no rational radius will ever do it. A radius of 1 gives an area of π, a radius of 10 gives 100π — always a multiple of π, never a plain integer. Working the other way round, entering an area of 100 gives a radius of 5.641896.

What is the difference between a chord, an arc and a segment?

A chord is a straight line joining two points on the circle; the diameter is the longest one there is. An arc is the curved part of the circumference between those same two points. A segment is the region between a chord and its arc, whereas a sector is the region between two radii and their arc. The distinction matters because the formulas are quite different.

Why is 360 degrees a full turn?

Convention inherited from Babylonian astronomy, which counted in sixties and used a 360-day year. It survives because 360 divides evenly by so much — 2, 3, 4, 5, 6, 8, 9, 10, 12 and more — which makes common fractions of a circle come out as whole numbers of degrees. Mathematics itself prefers radians, where a full turn is 2π, because that is the unit in which the calculus of circles behaves.

What are the formulas for a circle?

Three, and they all hang off the radius. The diameter is d = 2r. The circumference is C = 2πr, which is the same as πd. The area is A = πr². If you have any one of the four quantities you can recover the other three, which is what the mode buttons on this calculator do — enter a circumference or an area and it works backwards to the radius first.

Why does the area grow so much faster than the circumference?

Because area depends on the square of the radius and circumference only on the radius itself. Double the radius and the circumference doubles while the area quadruples; triple it and the area goes up ninefold. It is why a pizza twice the width is four times the food, and why the perimeter of a field grows far more slowly than the land inside it as the field gets bigger.

Circle with Radius 12

A circle of radius 12 has an area of 452.389342 and a circumference of 75.398224, with a diameter of 24. Both of those are exact multiples of π before they are turned into decimals — the area is 144π and the circumference is 24π — which is worth seeing, because it is where the irrationality lives. N...

CIRCLE CALCULATOR

SOLVE FROM

Radius (r)

Must be greater than 0

Central Angle θ (optional) — for arc length & sector area

RADIUS (r)

units

DIAMETER (d)

units

CIRCUMFERENCE (C)

75.398224

units

AREA (A)

452.389342

units²

STEP-BY-STEP

Given: radius r = 12

Diameter: d = 2r = 2 × 12 = 24

Circumference: C = 2πr = 2 × π × 12 = 75.398224

Area: A = πr² = π × 12² = 452.389342

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference12π × 2 = 75.398224

Areaπ × 12² = 452.389342

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 12 has an area of 452.389342 and a circumference of 75.398224. This page opens with the radius set to 12, so nothing needs typing.
2
Read the four result tiles — radius 12, diameter 24, circumference 75.398224 and area 452.389342. The STEPS panel underneath shows each one being derived rather than just asserted.
3
Add an angle to get a wedge. A 90° sector of this circle has an arc of 18.849556 and an area of 113.097336; a 60° sector has an arc of 12.566371 and an area of 75.398224.
4
Switch the input mode to run the same circle backwards — enter the area 452.389342 or the circumference 75.398224 and it recovers the radius 12, which is a useful check that everything is consistent.

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Last updated: July 28, 2026 · Formula verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.