What is the area of a circle with radius 4?

The area is 16π, which is 50.265482 square units. The formula is A = πr², so squaring the radius gives 4 × 4 = 16, and multiplying by π gives 50.265482. Because the radius squares, the area of this circle is 16 times that of the unit circle rather than 4 times.

What is the circumference of a circle with radius 4?

The circumference is 8π, or 25.132741 units. It comes from C = 2πr, so 2 × 4 = 8, then × π. The same circle has a diameter of 8, and since C = πd you can get there either way — 8π is the same as 8π. 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 4 than radius 3?

The radius goes up by 33.33%, from 3 to 4, but the area goes up by 77.78% — from 28.274334 to 50.265482. That is the square law: the area ratio is (4/3)² = 1.777778. The circumference, being linear, rises by the same 33.33% as the radius.

What fits inside a circle of radius 4?

A square inscribed in it has a diagonal equal to the diameter, 8, so its side is 4√2 = 5.656854 and its area is 2r² = 32 — 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 4, since the hexagon side always equals the radius, giving a perimeter of 24 against a circumference of 25.132741.

How good is 22/7 as an approximation?

22/7 is 3.142857, against a true π of 3.141593 — high by about 0.04%. For a circle of radius 7 it gives a circumference of exactly 44 where the truth is 43.982297. It survives because it is memorable and accurate enough for most hand calculation. 355/113 is far better, matching π to six decimal places, and is barely harder to remember.

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.

Circle with Radius 4

A circle of radius 4 has an area of 50.265482 and a circumference of 25.132741, with a diameter of 8. Both of those are exact multiples of π before they are turned into decimals — the area is 16π and the circumference is 8π — which is worth seeing, because it is where the irrationality lives. Neithe...

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)

25.132741

units

AREA (A)

50.265482

units²

STEP-BY-STEP

Given: radius r = 4

Diameter: d = 2r = 2 × 4 = 8

Circumference: C = 2πr = 2 × π × 4 = 25.132741

Area: A = πr² = π × 4² = 50.265482

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference4π × 2 = 25.132741

Areaπ × 4² = 50.265482

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 4 has an area of 50.265482 and a circumference of 25.132741. This page opens with the radius set to 4, so nothing needs typing.
2
Read the four result tiles — radius 4, diameter 8, circumference 25.132741 and area 50.265482. 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 6.283185 and an area of 12.566371; a 60° sector has an arc of 4.18879 and an area of 8.37758.
4
Switch the input mode to run the same circle backwards — enter the area 50.265482 or the circumference 25.132741 and it recovers the radius 4, which is a useful check that everything is consistent.

FREQUENTLY ASKED QUESTIONS

RELATED CALCULATORS

Right Triangle Calculator

Calculate instantly →

Circle with Radius 9 — Area and Circumference

Calculate instantly →

Circle with Radius 3 — Area and Circumference

Calculate instantly →

Circle with Radius 5 — Area and Circumference

Calculate instantly →

MORE GEOMETRY CALCULATORS

Circle Calculator

Calculate instantly →

Triangle Calculator

Calculate instantly →

Right Triangle Calculator

Calculate instantly →

Rectangle Calculator

Calculate instantly →

Sphere Calculator

Calculate instantly →

Slope Calculator

Calculate instantly →

Cylinder Calculator

Calculate instantly →

Slope Between Two Points Calculator

Calculate instantly →

Circle with Radius 1 — Area and Circumference

Calculate instantly →

Circle with Radius 2 — Area and Circumference

Calculate instantly →

Circle with Radius 3 — Area and Circumference

Calculate instantly →

Circle with Radius 5 — Area and Circumference

Calculate instantly →

Circle with Radius 6 — Area and Circumference

Calculate instantly →

Circle with Radius 7 — Area and Circumference

Calculate instantly →

Circle with Radius 8 — Area and Circumference

Calculate instantly →

Circle with Radius 9 — Area and Circumference

Calculate instantly →

Circle with Radius 10 — Area and Circumference

Calculate instantly →

Circle with Radius 11 — Area and Circumference

Calculate instantly →

Circle with Radius 12 — Area and Circumference

Calculate instantly →

Was this calculator helpful?

Last updated: July 28, 2026 · Formula verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.