What is the area of a circle with radius 8?

The area is 64π, which is 201.06193 square units. The formula is A = πr², so squaring the radius gives 8 × 8 = 64, and multiplying by π gives 201.06193. Because the radius squares, the area of this circle is 64 times that of the unit circle rather than 8 times.

What is the circumference of a circle with radius 8?

The circumference is 16π, or 50.265482 units. It comes from C = 2πr, so 2 × 8 = 16, then × π. The same circle has a diameter of 16, and since C = πd you can get there either way — 16π is the same as 16π. 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 8 than radius 7?

The radius goes up by 14.29%, from 7 to 8, but the area goes up by 30.61% — from 153.93804 to 201.06193. That is the square law: the area ratio is (8/7)² = 1.306122. The circumference, being linear, rises by the same 14.29% as the radius.

What fits inside a circle of radius 8?

A square inscribed in it has a diagonal equal to the diameter, 16, so its side is 8√2 = 11.313708 and its area is 2r² = 128 — 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 8, since the hexagon side always equals the radius, giving a perimeter of 48 against a circumference of 50.265482.

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.

How was π first calculated?

By squeezing. Archimedes inscribed and circumscribed regular polygons around a circle and computed both perimeters, knowing the true circumference lay between them. With 96-sided polygons he pinned π between 223/71 and 22/7 — that is, between 3.1408 and 3.1429. The method is exact in principle and only limited by how many sides you have the patience for.

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 8

A circle of radius 8 has an area of 201.06193 and a circumference of 50.265482, with a diameter of 16. Both of those are exact multiples of π before they are turned into decimals — the area is 64π and the circumference is 16π — which is worth seeing, because it is where the irrationality lives. Neit...

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)

50.265482

units

AREA (A)

201.06193

units²

STEP-BY-STEP

Given: radius r = 8

Diameter: d = 2r = 2 × 8 = 16

Circumference: C = 2πr = 2 × π × 8 = 50.265482

Area: A = πr² = π × 8² = 201.06193

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference8π × 2 = 50.265482

Areaπ × 8² = 201.06193

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 8 has an area of 201.06193 and a circumference of 50.265482. This page opens with the radius set to 8, so nothing needs typing.
2
Read the four result tiles — radius 8, diameter 16, circumference 50.265482 and area 201.06193. 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 12.566371 and an area of 50.265482; a 60° sector has an arc of 8.37758 and an area of 33.510322.
4
Switch the input mode to run the same circle backwards — enter the area 201.06193 or the circumference 50.265482 and it recovers the radius 8, 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.