What is the area of a circle with radius 18?

The area is 324π, which is 1,017.87602 square units. The formula is A = πr², so squaring the radius gives 18 × 18 = 324, and multiplying by π gives 1,017.87602. Because the radius squares, the area of this circle is 324 times that of the unit circle rather than 18 times.

What is the circumference of a circle with radius 18?

The circumference is 36π, or 113.097336 units. It comes from C = 2πr, so 2 × 18 = 36, then × π. The same circle has a diameter of 36, and since C = πd you can get there either way — 36π is the same as 36π. 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 18 than radius 17?

The radius goes up by 5.88%, from 17 to 18, but the area goes up by 12.11% — from 907.920277 to 1,017.87602. That is the square law: the area ratio is (18/17)² = 1.121107. The circumference, being linear, rises by the same 5.88% as the radius.

What fits inside a circle of radius 18?

A square inscribed in it has a diagonal equal to the diameter, 36, so its side is 18√2 = 25.455844 and its area is 2r² = 648 — 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 18, since the hexagon side always equals the radius, giving a perimeter of 108 against a circumference of 113.097336.

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.

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.

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.

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.

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.

Circle with Radius 18

A circle of radius 18 has an area of 1,017.87602 and a circumference of 113.097336, with a diameter of 36. Both of those are exact multiples of π before they are turned into decimals — the area is 324π and the circumference is 36π — which is worth seeing, because it is where the irrationality lives....

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)

113.097336

units

AREA (A)

1,017.87602

units²

STEP-BY-STEP

Given: radius r = 18

Diameter: d = 2r = 2 × 18 = 36

Circumference: C = 2πr = 2 × π × 18 = 113.097336

Area: A = πr² = π × 18² = 1,017.87602

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference18π × 2 = 113.097336

Areaπ × 18² = 1,017.87602

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 18 has an area of 1,017.87602 and a circumference of 113.097336. This page opens with the radius set to 18, so nothing needs typing.
2
Read the four result tiles — radius 18, diameter 36, circumference 113.097336 and area 1,017.87602. 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 28.274334 and an area of 254.469005; a 60° sector has an arc of 18.849556 and an area of 169.646003.
4
Switch the input mode to run the same circle backwards — enter the area 1,017.87602 or the circumference 113.097336 and it recovers the radius 18, 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.