What is the area of a circle with radius 6?

The area is 36π, which is 113.097336 square units. The formula is A = πr², so squaring the radius gives 6 × 6 = 36, and multiplying by π gives 113.097336. Because the radius squares, the area of this circle is 36 times that of the unit circle rather than 6 times.

What is the circumference of a circle with radius 6?

The circumference is 12π, or 37.699112 units. It comes from C = 2πr, so 2 × 6 = 12, then × π. The same circle has a diameter of 12, and since C = πd you can get there either way — 12π is the same as 12π. 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 6 than radius 5?

The radius goes up by 20%, from 5 to 6, but the area goes up by 44% — from 78.539816 to 113.097336. That is the square law: the area ratio is (6/5)² = 1.44. The circumference, being linear, rises by the same 20% as the radius.

What fits inside a circle of radius 6?

A square inscribed in it has a diagonal equal to the diameter, 12, so its side is 6√2 = 8.485281 and its area is 2r² = 72 — 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 6, since the hexagon side always equals the radius, giving a perimeter of 36 against a circumference of 37.699112.

What is a sector and how do I find its area?

A sector is a wedge of the circle bounded by two radii and the arc between them. Its area is the fraction of the full circle the angle covers: A = (θ ÷ 360) × πr² for an angle in degrees. The arc length works the same way, as (θ ÷ 360) × 2πr. Enter an angle in the calculator and both appear, since both are simply a proportion of the whole.

What shapes fit inside a circle?

A square inscribed in a circle of radius r has a diagonal of 2r, so its side is r√2 and its area 2r² — which is about 64% of the circle. A regular hexagon is tidier: its side equals the radius exactly, which is why stepping a compass round a circle at its own setting divides it into six. The more sides a regular polygon has, the closer its area creeps to πr² without ever reaching it.

How does a circle relate to a sphere of the same radius?

Closely, and in a way worth remembering. A sphere’s surface area is 4πr², exactly four times the area of the circle through its middle. Its volume is (4/3)πr³. Archimedes was pleased enough with the related result — that a sphere is two thirds of the cylinder that encloses it — to have it carved on his tombstone.

Why are circles measured from the centre?

Because the radius is what defines the shape: a circle is the set of all points a fixed distance from one point, and that distance is the radius. Every other quantity follows from it. The diameter is convenient for measuring a physical object, since you can lay a ruler across it without finding the centre first, which is why pipes and drills are specified by diameter while the mathematics runs on radius.

What units does this calculator use?

Whatever you like — it is unit-agnostic. Enter a radius in centimetres and the circumference comes back in centimetres and the area in square centimetres. The only rule is consistency: the answer carries whatever unit you put in, and area carries it squared. That is why the results are labelled "units" and "units²" rather than being tied to any particular system.

Circle with Radius 6

A circle of radius 6 has an area of 113.097336 and a circumference of 37.699112, with a diameter of 12. Both of those are exact multiples of π before they are turned into decimals — the area is 36π and the circumference is 12π — which is worth seeing, because it is where the irrationality lives. Nei...

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)

37.699112

units

AREA (A)

113.097336

units²

STEP-BY-STEP

Given: radius r = 6

Diameter: d = 2r = 2 × 6 = 12

Circumference: C = 2πr = 2 × π × 6 = 37.699112

Area: A = πr² = π × 6² = 113.097336

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference6π × 2 = 37.699112

Areaπ × 6² = 113.097336

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 6 has an area of 113.097336 and a circumference of 37.699112. This page opens with the radius set to 6, so nothing needs typing.
2
Read the four result tiles — radius 6, diameter 12, circumference 37.699112 and area 113.097336. 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 9.424778 and an area of 28.274334; a 60° sector has an arc of 6.283185 and an area of 18.849556.
4
Switch the input mode to run the same circle backwards — enter the area 113.097336 or the circumference 37.699112 and it recovers the radius 6, 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.