What is the area of a circle with radius 20?

The area is 400π, which is 1,256.637061 square units. The formula is A = πr², so squaring the radius gives 20 × 20 = 400, and multiplying by π gives 1,256.637061. Because the radius squares, the area of this circle is 400 times that of the unit circle rather than 20 times.

What is the circumference of a circle with radius 20?

The circumference is 40π, or 125.663706 units. It comes from C = 2πr, so 2 × 20 = 40, then × π. The same circle has a diameter of 40, and since C = πd you can get there either way — 40π is the same as 40π. 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 20 than radius 19?

The radius goes up by 5.26%, from 19 to 20, but the area goes up by 10.8% — from 1,134.114948 to 1,256.637061. That is the square law: the area ratio is (20/19)² = 1.108033. The circumference, being linear, rises by the same 5.26% as the radius.

What fits inside a circle of radius 20?

A square inscribed in it has a diagonal equal to the diameter, 40, so its side is 20√2 = 28.284271 and its area is 2r² = 800 — 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 20, since the hexagon side always equals the radius, giving a perimeter of 120 against a circumference of 125.663706.

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.

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.

Circle with Radius 20

A circle of radius 20 has an area of 1,256.637061 and a circumference of 125.663706, with a diameter of 40. Both of those are exact multiples of π before they are turned into decimals — the area is 400π and the circumference is 40π — 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)

125.663706

units

AREA (A)

1,256.637061

units²

STEP-BY-STEP

Given: radius r = 20

Diameter: d = 2r = 2 × 20 = 40

Circumference: C = 2πr = 2 × π × 20 = 125.663706

Area: A = πr² = π × 20² = 1,256.637061

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference20π × 2 = 125.663706

Areaπ × 20² = 1,256.637061

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 20 has an area of 1,256.637061 and a circumference of 125.663706. This page opens with the radius set to 20, so nothing needs typing.
2
Read the four result tiles — radius 20, diameter 40, circumference 125.663706 and area 1,256.637061. 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 31.415927 and an area of 314.159265; a 60° sector has an arc of 20.943951 and an area of 209.43951.
4
Switch the input mode to run the same circle backwards — enter the area 1,256.637061 or the circumference 125.663706 and it recovers the radius 20, 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.