What is the area of a circle with radius 1?

The area is 1π, which is 3.141593 square units. The formula is A = πr², so squaring the radius gives 1 × 1 = 1, and multiplying by π gives 3.141593. Because the radius squares, the area of this circle is 1 times that of the unit circle rather than 1 times.

What is the circumference of a circle with radius 1?

The circumference is 2π, or 6.283185 units. It comes from C = 2πr, so 2 × 1 = 2, then × π. The same circle has a diameter of 2, and since C = πd you can get there either way — 2π is the same as 2π. 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 1 than radius 1?

Radius 1 is the reference every other circle is measured against. Its area is exactly π = 3.141593 and its circumference exactly 2π = 6.283185, so a circle of radius r has r² times this area and r times this circumference.

What fits inside a circle of radius 1?

A square inscribed in it has a diagonal equal to the diameter, 2, so its side is 1√2 = 1.414214 and its area is 2r² = 2 — 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 1, since the hexagon side always equals the radius, giving a perimeter of 6 against a circumference of 6.283185.

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.

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.

Circle with Radius 1

A circle of radius 1 has an area of 3.141593 and a circumference of 6.283185, with a diameter of 2. Both of those are exact multiples of π before they are turned into decimals — the area is 1π and the circumference is 2π — which is worth seeing, because it is where the irrationality lives. Neither f...

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)

6.283185

units

AREA (A)

3.141593

units²

STEP-BY-STEP

Given: radius r = 1

Diameter: d = 2r = 2 × 1 = 2

Circumference: C = 2πr = 2 × π × 1 = 6.283185

Area: A = πr² = π × 1² = 3.141593

QUICK EXAMPLES

LIVE DIAGRAM

EXACT EXPRESSIONS

Circumference1π × 2 = 6.283185

Areaπ × 1² = 3.141593

C/d ratioπ = 3.14159265...

Created with❤️byeaglecalculator.com

HOW TO USE

1
The answer is already here: a circle of radius 1 has an area of 3.141593 and a circumference of 6.283185. This page opens with the radius set to 1, so nothing needs typing.
2
Read the four result tiles — radius 1, diameter 2, circumference 6.283185 and area 3.141593. 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 1.570796 and an area of 0.785398; a 60° sector has an arc of 1.047198 and an area of 0.523599.
4
Switch the input mode to run the same circle backwards — enter the area 3.141593 or the circumference 6.283185 and it recovers the radius 1, 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.