What is the area of a circle with radius 5?

The area is 25π, which is 78.539816 square units. The formula is A = πr², so squaring the radius gives 5 × 5 = 25, and multiplying by π gives 78.539816. Because the radius squares, the area of this circle is 25 times that of the unit circle rather than 5 times.

What is the circumference of a circle with radius 5?

The circumference is 10π, or 31.415927 units. It comes from C = 2πr, so 2 × 5 = 10, then × π. The same circle has a diameter of 10, and since C = πd you can get there either way — 10π is the same as 10π. 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 5 than radius 4?

The radius goes up by 25%, from 4 to 5, but the area goes up by 56.25% — from 50.265482 to 78.539816. That is the square law: the area ratio is (5/4)² = 1.5625. The circumference, being linear, rises by the same 25% as the radius.

What fits inside a circle of radius 5?

A square inscribed in it has a diagonal equal to the diameter, 10, so its side is 5√2 = 7.071068 and its area is 2r² = 50 — 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 5, since the hexagon side always equals the radius, giving a perimeter of 30 against a circumference of 31.415927.

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 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.

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.

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.

Circle with Radius 5

A circle of radius 5 has an area of 78.539816 and a circumference of 31.415927, with a diameter of 10. Both of those are exact multiples of π before they are turned into decimals — the area is 25π and the circumference is 10π — 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)

31.415927

units

AREA (A)

78.539816

units²

STEP-BY-STEP

Given: radius r = 5

Diameter: d = 2r = 2 × 5 = 10

Circumference: C = 2πr = 2 × π × 5 = 31.415927

Area: A = πr² = π × 5² = 78.539816

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference5π × 2 = 31.415927

Areaπ × 5² = 78.539816

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 5 has an area of 78.539816 and a circumference of 31.415927. This page opens with the radius set to 5, so nothing needs typing.
2
Read the four result tiles — radius 5, diameter 10, circumference 31.415927 and area 78.539816. 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 7.853982 and an area of 19.634954; a 60° sector has an arc of 5.235988 and an area of 13.089969.
4
Switch the input mode to run the same circle backwards — enter the area 78.539816 or the circumference 31.415927 and it recovers the radius 5, 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.