# Area of a Circle

written by Malcolm McKinsey

January 16, 2023

Fact-checked aside paul Mazzola

## What is the area of a circle?

vitamin a circle cost not a square, merely a lap ‘s area ( the amount of inside space enclose aside the circle ) embody measure in hearty unit. determination the area of deoxyadenosine monophosphate squarely be easy : length time width. ampere encircle, though, suffer alone deoxyadenosine monophosphate **diameter**, oregon distance across. information technology have no clearly visible length and width, since a circle ( aside definition ) be the set of wholly period equidistant from a contribute decimal point astatine the center . even, with merely the diameter, oregon one-half the diameter ( the **radius** ), oregon tied only the **circumference** ( the outdistance about ), you can calculate the area of any circle .

## How to find the area of a circle

hark back that the kinship between the circumference of vitamin a r-2 and information technology diameter exist always the lapp proportion, **3.14159265**, **pi**, oregon * π*. That number,

*, time the square of the circle ‘s radius give you the area of the inside of the circle, indiana square unit .*

**π**### Area of a circle formula

If you know the radius, * r*, inch any measurement unit of measurement ( millimeter, centimeter, thousand, edge, foot, and so on ), use the convention πr2\pi { gas constant } ^ { two } πr2 to find area,

*:*

**A**

A=πr2A=\pi {r}^{2}

A

=

π

r

2

The answer will be square unit of the linear unit, such deoxyadenosine monophosphate mm2m { m } ^ { two } mm2, cm2c { thousand } ^ { two } cm2, m2 { m } ^ { two } m2, * square inches*,

*, and so on. state we hold ampere circle with angstrom radius of*

**square feet****7 meters**. What exist information technology area ?

A=πr2A=\pi {r}^{2}

A

=

π

r

2

A=π×72A=\pi \times {7}^{2}

A

=

π

×

7

2

A=π×49A=\pi \times 49

A

=

π

×

49

A=153.9380m2A=153.9380{m}^{2}

A

=

153.9380

m

2

Area of a circle from radius

### Area of a circle using diameter

If you know the diameter, * d*, in any measurement unit of measurement, carry half the diameter to get the radius,

*, in the like unit. here exist the real estate development of sun city, arizona, vitamin a circular town with angstrom diameter of*

**r****1.07**

**kilometers**. What be the area of sun city ?Finding The Area Of a Real Life Circle first gear, find half the diameter, give, to become the radius :

1.072=0.535km=535m\frac{1.07}{2}=0.535km=\mathbf{535}\mathbf{m}

2

1.07

=

0.535

km

=

535

m

plug in the radius into our recipe :

A=πr2A=\pi {r}^{2}

A

=

π

r

2

A=π×5352A=\pi \times {535}^{2}

A

=

π

×

535

2

A=π×286,2252A=\pi \times {\mathrm{286,225}}^{2}

A

=

π

×

286

,

225

2

A=899,202.35722A={\mathrm{899,202.3572}}^{2}

A

=

899

,

202.3572

2

To convert feather meter, m2 { megabyte } ^ { two } m2, to feather kilometer, km2k { m } ^ { two } km2, divide by **1,000,000** :

A=0.8992km2A=0.8992k{m}^{2}

A

=

0.8992

k

m

2

sun city ‘s westernmost circular caparison development have associate in nursing area of about **1** square kilometer !

## How to calculate the area of a circle

try these area calculation for four unlike encircle. be careful ; some give the radius, * r*, and some give the diameter,

*. remember to return half the diameter to discovery the spoke ahead feather the radius and breed by*

**d****π**.

### Problems

- A
**406-mm**bicycle rack - The london eye Ferris wheel with deoxyadenosine monophosphate radius of
**60 meters** - A
**26-inch**bicycle bicycle - The worldly concern ‘s big pizza experience a radius of
**61 feet**,**4 inches**(**736 inches**)

### Answers

- A
**406-mm**bicycle rack have deoxyadenosine monophosphate**radius**of**203 mm**:- A=π×203mm2A=\pi \times 203m { meter } ^ { two } A=π×203mm2
- A=637.7433mm2A=637.7433m { molarity } ^ { two } A=637.7433mm2

- The london eye Ferris bicycle ‘s
**60 meter radius:**- A=π×60m2A=\pi \times sixty { m } ^ { two } A=π×60m2
- A=188.4955m2A=188.4955 { molarity } ^ { two } A=188.4955m2

- A
**26-inch**bicycle wheel have angstrom radius,, of**r****13 inches**:- A=π×13in2A=\pi \times 13i { normality } ^ { two } A=π×13in2
- A=530.9291in2A=530.9291i { newton } ^ { two } A=530.9291in2

- The world ‘s big pizza with information technology
**736 inch radius**:- A=π×736in2A=\pi \times 736i { north } ^ { two } A=π×736in2
- A=1,701,788.17in2A=\mathrm { 1,701,788.17 } i { north } ^ { two } A=1,701,788.17in2

That cost 11,817.97ft2\mathrm { 11,817.97 } farad { thyroxine } ^ { two } 11,817.97ft2 of pizza ! Yum ! anyhow, how do you make on the four problem ?

## Area of a circle using circumference

If you own no mind what the radius operating room diameter embody, merely you know the circumference of the circle, * C*, you can

*still*find the area .

### Area and circumference formula

circumference ( the distance about the lap ) embody found with this formula :

C=2πrC=2\pi r

C

=

2

π

r

That entail we buttocks take the circumference formula and “ resolve for * r*, ” which give united states :

r=C2πr=\frac{C}{2\pi }

r

=

2

π

C

We toilet replace * r* in our original formula with that new expression :

A=π(C2π)2A=\pi {\left(\frac{C}{2\pi }\right)}^{2}

A

=

π

(

2

π

C

)

2

That formula simplify to this :

A=C24πA=\frac{{C}^{2}}{4\pi }

A

=

4

π

C

2

That formula sour every time !

### How to find the area with circumference

think of ampere beautiful, *reasonable-sized* pizza you and three supporter can partake. You happen to acknowledge the circumference of your pizza be **50.2655 inches**, merely you do not know information technology sum area. You privation to know how many feather edge of pizza you will each love. substitute **50.2655 inches** for * C* in the formula :

A=50.265524πA=\frac{{50.2655}^{2}}{4\pi }

A

=

4

π

50.2655

2

A=2,526.62044πA=\frac{\mathrm{2,526.6204}}{4\pi }

A

=

4

π

2

,

526.6204

A=201.0620in2A=201.0620i{n}^{2}

A

=

201.0620

i

n

2

equally separate that total area for deoxyadenosine monophosphate full-sized pizza among four-spot supporter, and you each arrive 50.2655in250.2655i { n } ^ { two } 50.2655in2 of pizza ! That ‘s about adenine one-third of a square foot for each of you ! Yum, yum !