What is the area of a circle with radius 15?

The area is 225π, which is 706.858347 square units. The formula is A = πr², so squaring the radius gives 15 × 15 = 225, and multiplying by π gives 706.858347. Because the radius squares, the area of this circle is 225 times that of the unit circle rather than 15 times.

What is the circumference of a circle with radius 15?

The circumference is 30π, or 94.24778 units. It comes from C = 2πr, so 2 × 15 = 30, then × π. The same circle has a diameter of 30, and since C = πd you can get there either way — 30π is the same as 30π. 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 15 than radius 14?

The radius goes up by 7.14%, from 14 to 15, but the area goes up by 14.8% — from 615.75216 to 706.858347. That is the square law: the area ratio is (15/14)² = 1.147959. The circumference, being linear, rises by the same 7.14% as the radius.

What fits inside a circle of radius 15?

A square inscribed in it has a diagonal equal to the diameter, 30, so its side is 15√2 = 21.213203 and its area is 2r² = 450 — 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 15, since the hexagon side always equals the radius, giving a perimeter of 90 against a circumference of 94.24778.

What are the formulas for a circle?

Three, and they all hang off the radius. The diameter is d = 2r. The circumference is C = 2πr, which is the same as πd. The area is A = πr². If you have any one of the four quantities you can recover the other three, which is what the mode buttons on this calculator do — enter a circumference or an area and it works backwards to the radius first.

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 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 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.

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.

Circle with Radius 15

A circle of radius 15 has an area of 706.858347 and a circumference of 94.24778, with a diameter of 30. Both of those are exact multiples of π before they are turned into decimals — the area is 225π and the circumference is 30π — which is worth seeing, because it is where the irrationality lives. Ne...

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)

94.24778

units

AREA (A)

706.858347

units²

STEP-BY-STEP

Given: radius r = 15

Diameter: d = 2r = 2 × 15 = 30

Circumference: C = 2πr = 2 × π × 15 = 94.24778

Area: A = πr² = π × 15² = 706.858347

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference15π × 2 = 94.24778

Areaπ × 15² = 706.858347

C/d ratioπ = 3.14159265...

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HOW TO USE

1
The answer is already here: a circle of radius 15 has an area of 706.858347 and a circumference of 94.24778. This page opens with the radius set to 15, so nothing needs typing.
2
Read the four result tiles — radius 15, diameter 30, circumference 94.24778 and area 706.858347. 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 23.561945 and an area of 176.714587; a 60° sector has an arc of 15.707963 and an area of 117.809725.
4
Switch the input mode to run the same circle backwards — enter the area 706.858347 or the circumference 94.24778 and it recovers the radius 15, 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.