What is the area of a circle with radius 9?

The area is 81π, which is 254.469005 square units. The formula is A = πr², so squaring the radius gives 9 × 9 = 81, and multiplying by π gives 254.469005. Because the radius squares, the area of this circle is 81 times that of the unit circle rather than 9 times.

What is the circumference of a circle with radius 9?

The circumference is 18π, or 56.548668 units. It comes from C = 2πr, so 2 × 9 = 18, then × π. The same circle has a diameter of 18, and since C = πd you can get there either way — 18π is the same as 18π. 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 9 than radius 8?

The radius goes up by 12.5%, from 8 to 9, but the area goes up by 26.56% — from 201.06193 to 254.469005. That is the square law: the area ratio is (9/8)² = 1.265625. The circumference, being linear, rises by the same 12.5% as the radius.

What fits inside a circle of radius 9?

A square inscribed in it has a diagonal equal to the diameter, 18, so its side is 9√2 = 12.727922 and its area is 2r² = 162 — 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 9, since the hexagon side always equals the radius, giving a perimeter of 54 against a circumference of 56.548668.

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.

What is the difference between a chord, an arc and a segment?

A chord is a straight line joining two points on the circle; the diameter is the longest one there is. An arc is the curved part of the circumference between those same two points. A segment is the region between a chord and its arc, whereas a sector is the region between two radii and their arc. The distinction matters because the formulas are quite different.

Circle with Radius 9

A circle of radius 9 has an area of 254.469005 and a circumference of 56.548668, with a diameter of 18. Both of those are exact multiples of π before they are turned into decimals — the area is 81π and the circumference is 18π — 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)

56.548668

units

AREA (A)

254.469005

units²

STEP-BY-STEP

Given: radius r = 9

Diameter: d = 2r = 2 × 9 = 18

Circumference: C = 2πr = 2 × π × 9 = 56.548668

Area: A = πr² = π × 9² = 254.469005

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference9π × 2 = 56.548668

Areaπ × 9² = 254.469005

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 9 has an area of 254.469005 and a circumference of 56.548668. This page opens with the radius set to 9, so nothing needs typing.
2
Read the four result tiles — radius 9, diameter 18, circumference 56.548668 and area 254.469005. 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 14.137167 and an area of 63.617251; a 60° sector has an arc of 9.424778 and an area of 42.411501.
4
Switch the input mode to run the same circle backwards — enter the area 254.469005 or the circumference 56.548668 and it recovers the radius 9, 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.