Area of a Circle

Reckoner

Enter the radius, bore, circumference or area of a Circle to find the other three. The calculations are washed "live":

images/circumvolve-dia-circ.js

How to Calculate the Area

The area of a circle is:

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

or, when you know the Diameter: A = (π/iv) × Dii

or, when y'all know the Circumference: A = C2 / ivπ

Example: What is the area of a circle with radius of 3 grand ?

circle radius 3

Radius = r = 3

Area = π r2

= π × 32

= three.14159... × (3 × three)

= 28.27 yard2 (to 2 decimal places)

How to Remember?

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

Comparing a Circle to a Square

It is interesting to compare the area of a circumvolve to a foursquare:

circle area is about 80% of square

A circle has about 80% of the surface area of a like-width foursquare.
The actual value is (π/iv) = 0.785398... = 78.5398...%

Why? Considering the Square's Expanse is w2
and the Circle's Area is (π/iv) × wii

Case: Compare a square to a circumvolve of width 3 thousand

Square's Area = westward2 = 3ii = 9 m2

Estimate of Circle'southward Area = fourscore% of Square'due south Area = 80% of ix = 7.2 mtwo

Circle's True Area = (π/4) × D2 = (π/4) × threeii = 7.07 10002 (to ii decimals)

The gauge of seven.2 m2 is not far off 7.07 one thousand2

A "Real World" Case

Example: Max is building a house. The start step is to drill holes and fill them with concrete.

The holes are 0.iv m wide and ane k deep, how much physical should Max order for each hole?

circle auger

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

The diameter is 0.4m, and then the Area is:

circle area example

A = (π/4) × Dtwo

A = (3.14159.../4) × 0.42

A = 0.7854... × 0.xvi

A = 0.126 thousand2 (to 3 decimals)

And the holes are ane m deep, and then:

Volume = 0.126 10002 × i m = 0.126 chiliad3

And then Max should society 0.126 cubic meters of physical to fill each pigsty.

Notation: Max could have estimated the area by:

  • 1. Calculating a foursquare pigsty: 0.4 × 0.4 = 0.xvi m2
  • 2. Taking eighty% of that (estimates a circle): 80% × 0.16 chiliadtwo = 0.128 m2
  • 3. And the volume of a 1 m deep hole is: 0.128 miii

And something interesting for yous:

See Circle Area by Lines