What is the area of a circle with radius 16?

The area is 256π, which is 804.247719 square units. The formula is A = πr², so squaring the radius gives 16 × 16 = 256, and multiplying by π gives 804.247719. Because the radius squares, the area of this circle is 256 times that of the unit circle rather than 16 times.

What is the circumference of a circle with radius 16?

The circumference is 32π, or 100.530965 units. It comes from C = 2πr, so 2 × 16 = 32, then × π. The same circle has a diameter of 32, and since C = πd you can get there either way — 32π is the same as 32π. 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 16 than radius 15?

The radius goes up by 6.67%, from 15 to 16, but the area goes up by 13.78% — from 706.858347 to 804.247719. That is the square law: the area ratio is (16/15)² = 1.137778. The circumference, being linear, rises by the same 6.67% as the radius.

What fits inside a circle of radius 16?

A square inscribed in it has a diagonal equal to the diameter, 32, so its side is 16√2 = 22.627417 and its area is 2r² = 512 — 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 16, since the hexagon side always equals the radius, giving a perimeter of 96 against a circumference of 100.530965.

Why does the area grow so much faster than the circumference?

Because area depends on the square of the radius and circumference only on the radius itself. Double the radius and the circumference doubles while the area quadruples; triple it and the area goes up ninefold. It is why a pizza twice the width is four times the food, and why the perimeter of a field grows far more slowly than the land inside it as the field gets bigger.

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.

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.

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.

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.

Circle with Radius 16

A circle of radius 16 has an area of 804.247719 and a circumference of 100.530965, with a diameter of 32. Both of those are exact multiples of π before they are turned into decimals — the area is 256π and the circumference is 32π — which is worth seeing, because it is where the irrationality lives. ...

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)

100.530965

units

AREA (A)

804.247719

units²

STEP-BY-STEP

Given: radius r = 16

Diameter: d = 2r = 2 × 16 = 32

Circumference: C = 2πr = 2 × π × 16 = 100.530965

Area: A = πr² = π × 16² = 804.247719

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference16π × 2 = 100.530965

Areaπ × 16² = 804.247719

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 16 has an area of 804.247719 and a circumference of 100.530965. This page opens with the radius set to 16, so nothing needs typing.
2
Read the four result tiles — radius 16, diameter 32, circumference 100.530965 and area 804.247719. 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 25.132741 and an area of 201.06193; a 60° sector has an arc of 16.755161 and an area of 134.041287.
4
Switch the input mode to run the same circle backwards — enter the area 804.247719 or the circumference 100.530965 and it recovers the radius 16, 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.