Area of a Circle

Calculator

Enter the radius, diameter, circumference or area of a Circle to detect the other three. The calculations are done "live":

images/circle-dia-circ.js

How to Calculate the Surface area

The area of a circumvolve is:

π (Pi) times the Radius squared: A = π r2

or, when y'all know the Diameter: A = (π/4) × Dtwo

or, when you know the Circumference: A = C2 / 4π

Example: What is the expanse of a circle with radius of 3 g ?

circle radius 3

Radius = r = 3

Expanse = π r2

= π × 32

= 3.14159... × (3 × 3)

= 28.27 thou2 (to ii decimal places)

How to Remember?

circle area pi r-squared (but pies are round!)
To help you retrieve recall "Pie Are Squared"
(even though pies are usually round)

Comparing a Circle to a Square

It is interesting to compare the area of a circle to a square:

circle area is about 80% of square

A circle has about 80% of the expanse of a similar-width square.
The actual value is (π/iv) = 0.785398... = 78.5398...%

Why? Because the Square's Expanse is w2
and the Circle's Surface area is (π/4) × due west2

Example: Compare a square to a circle of width three yard

Foursquare'due south Area = wtwo = iii2 = nine m2

Estimate of Circle'south Expanse = eighty% of Foursquare's Area = 80% of nine = 7.two mii

Circle'south Truthful Area = (π/4) × D2 = (π/4) × 32 = vii.07 k2 (to 2 decimals)

The estimate of 7.2 mtwo is not far off seven.07 mtwo

A "Real World" Example

Instance: Max is building a house. The first stride is to drill holes and fill them with concrete.

The holes are 0.4 yard wide and 1 yard deep, how much concrete should Max social club for each hole?

circle auger

The holes are circular (in cross section) because they are drilled out using an auger.

The diameter is 0.4m, so the Area is:

circle area example

A = (π/iv) × D2

A = (3.14159.../4) × 0.42

A = 0.7854... × 0.16

A = 0.126 mii (to 3 decimals)

And the holes are 1 one thousand deep, so:

Volume = 0.126 thousand2 × 1 m = 0.126 chiliad3

So Max should order 0.126 cubic meters of physical to make full each hole.

Note: Max could have estimated the area past:

  • 1. Calculating a square hole: 0.four × 0.4 = 0.sixteen mii
  • 2. Taking fourscore% of that (estimates a circle): fourscore% × 0.16 ktwo = 0.128 m2
  • 3. And the volume of a i m deep hole is: 0.128 mthree

And something interesting for you:

Come across Circumvolve Expanse by Lines