What is the area of a circle with radius 3?

The area is 9π, which is 28.274334 square units. The formula is A = πr², so squaring the radius gives 3 × 3 = 9, and multiplying by π gives 28.274334. Because the radius squares, the area of this circle is 9 times that of the unit circle rather than 3 times.

What is the circumference of a circle with radius 3?

The circumference is 6π, or 18.849556 units. It comes from C = 2πr, so 2 × 3 = 6, then × π. The same circle has a diameter of 6, and since C = πd you can get there either way — 6π is the same as 6π. 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 3 than radius 2?

The radius goes up by 50%, from 2 to 3, but the area goes up by 125% — from 12.566371 to 28.274334. That is the square law: the area ratio is (3/2)² = 2.25. The circumference, being linear, rises by the same 50% as the radius.

What fits inside a circle of radius 3?

A square inscribed in it has a diagonal equal to the diameter, 6, so its side is 3√2 = 4.242641 and its area is 2r² = 18 — 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 3, since the hexagon side always equals the radius, giving a perimeter of 18 against a circumference of 18.849556.

The ratio of any circle’s circumference to its diameter — the same number for every circle, which is the surprising part and the reason it earned a name. It is irrational, so it has no exact decimal or fraction, and transcendental, which is what makes squaring the circle with compass and straightedge impossible. To eight places it is 3.14159265.

How good is 22/7 as an approximation?

22/7 is 3.142857, against a true π of 3.141593 — high by about 0.04%. For a circle of radius 7 it gives a circumference of exactly 44 where the truth is 43.982297. It survives because it is memorable and accurate enough for most hand calculation. 355/113 is far better, matching π to six decimal places, and is barely harder to remember.

How do I find the area from the circumference?

Work back to the radius first. From C = 2πr you get r = C ÷ 2π, and then A = πr². Substituting gives a direct route, A = C² ÷ 4π, which saves a step. This calculator does exactly that when you switch the input mode to circumference — it recovers the radius, then derives everything else from it, so every quantity stays consistent.

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.

Circle with Radius 3

A circle of radius 3 has an area of 28.274334 and a circumference of 18.849556, with a diameter of 6. Both of those are exact multiples of π before they are turned into decimals — the area is 9π and the circumference is 6π — which is worth seeing, because it is where the irrationality lives. Neither...

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)

18.849556

units

AREA (A)

28.274334

units²

STEP-BY-STEP

Given: radius r = 3

Diameter: d = 2r = 2 × 3 = 6

Circumference: C = 2πr = 2 × π × 3 = 18.849556

Area: A = πr² = π × 3² = 28.274334

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference3π × 2 = 18.849556

Areaπ × 3² = 28.274334

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 3 has an area of 28.274334 and a circumference of 18.849556. This page opens with the radius set to 3, so nothing needs typing.
2
Read the four result tiles — radius 3, diameter 6, circumference 18.849556 and area 28.274334. 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 4.712389 and an area of 7.068583; a 60° sector has an arc of 3.141593 and an area of 4.712389.
4
Switch the input mode to run the same circle backwards — enter the area 28.274334 or the circumference 18.849556 and it recovers the radius 3, 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.