What is the area of a circle with radius 14?

The area is 196π, which is 615.75216 square units. The formula is A = πr², so squaring the radius gives 14 × 14 = 196, and multiplying by π gives 615.75216. Because the radius squares, the area of this circle is 196 times that of the unit circle rather than 14 times.

What is the circumference of a circle with radius 14?

The circumference is 28π, or 87.964594 units. It comes from C = 2πr, so 2 × 14 = 28, then × π. The same circle has a diameter of 28, and since C = πd you can get there either way — 28π is the same as 28π. 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 14 than radius 13?

The radius goes up by 7.69%, from 13 to 14, but the area goes up by 15.98% — from 530.929158 to 615.75216. That is the square law: the area ratio is (14/13)² = 1.159763. The circumference, being linear, rises by the same 7.69% as the radius.

What fits inside a circle of radius 14?

A square inscribed in it has a diagonal equal to the diameter, 28, so its side is 14√2 = 19.79899 and its area is 2r² = 392 — 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 14, since the hexagon side always equals the radius, giving a perimeter of 84 against a circumference of 87.964594.

Why is 360 degrees a full turn?

Convention inherited from Babylonian astronomy, which counted in sixties and used a 360-day year. It survives because 360 divides evenly by so much — 2, 3, 4, 5, 6, 8, 9, 10, 12 and more — which makes common fractions of a circle come out as whole numbers of degrees. Mathematics itself prefers radians, where a full turn is 2π, because that is the unit in which the calculus of circles behaves.

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.

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.

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 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.

Circle with Radius 14

A circle of radius 14 has an area of 615.75216 and a circumference of 87.964594, with a diameter of 28. Both of those are exact multiples of π before they are turned into decimals — the area is 196π and the circumference is 28π — 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)

87.964594

units

AREA (A)

615.75216

units²

STEP-BY-STEP

Given: radius r = 14

Diameter: d = 2r = 2 × 14 = 28

Circumference: C = 2πr = 2 × π × 14 = 87.964594

Area: A = πr² = π × 14² = 615.75216

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference14π × 2 = 87.964594

Areaπ × 14² = 615.75216

C/d ratioπ = 3.14159265...

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HOW TO USE

1
The answer is already here: a circle of radius 14 has an area of 615.75216 and a circumference of 87.964594. This page opens with the radius set to 14, so nothing needs typing.
2
Read the four result tiles — radius 14, diameter 28, circumference 87.964594 and area 615.75216. 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 21.991149 and an area of 153.93804; a 60° sector has an arc of 14.660766 and an area of 102.62536.
4
Switch the input mode to run the same circle backwards — enter the area 615.75216 or the circumference 87.964594 and it recovers the radius 14, 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.