ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

What is Pi and How is it Used?

Updated on October 7, 2014

Pi is a Ratio

Firstly let me explain that Pi is what Mathematician's term an, "irrational number." This simply means that it is a number that does not lend itself to concrete, exact expression in it's decimal form but rather goes on to infinity. Pi can be presented quite rationally as 22/7 but try dividing 22 by 7 on a calculator and you'll see you get a number that never actually ends. As it's decimal places become more and more minute the number simply keeps going and going. You'll end up with 3.14285714.....on to infinity. The number never actually specifies itself perfectly and is thus called irrational.

This point aside the most important thing to remember about Pi is that is represents a ratio. Specifically this is a ratio that pertains to all circles. Recall that the definition of a circle is a two-dimensional curve with every point on the curve being the same distance from a central fixed point. It stands to reason that if we consider all such perfect circles, from the tiniest to the largest, there must be some constant and consistent relationship between the diameter of a circle (a straight line beginning at one point along the curved edge running through the central point and ending at the opposite point along the curved edge.) and the circumference. The circumference is the the curved line that defines the outer edge of the circle. See the diagrams at the side for a visual representation of a diameter and a circumference. You should also notice that the Radius is always exactly 1/2 of the diameter or conversely that the diameter is always twice the radius.

If you are following me thus far, great. Now as I was saying it stands to reason that as the diameter increases the total length of the bold curved line that defines the circle, the circumference, will change in a consistent way in relation to the diameter. And it turns out it does. The relationship between the diameter of a circle and the circumference of a circle is a ratio called Pi or 3.14.... In other words when the diameter is 1 unit the circumference will be 3.14 units. If the diameter is two units then the circumference is 2(Pi) or 2(3.14) or 6.28 units. This relationship hold for whatever the length of the diameter might be whether 1835.23 m or 13.567 in. Simply multiple the length of the diameter by Pi, be sure to keep the units the same, and you will easily find the circumference or length of the outer edge of the circle.

How Pi is used in Geometry Problems

Pi is used in two-dimensional geometry to either find the circumference or the area of a circle.

For example let's say we are given the length of the radius of a circle as 3.5 ft. and asked to find the circumference of the circle. The formula we will use in 2(r)Pi=C where r=3.5, Pi equals 3.14, and C= our unknown circumference. The reason why we are multiply the radius by 2 should be fairly obvious if you remember that a radius is always one half of a diameter (again refer to the diagrams to the right). We plug these number in and get



C=21.98 ft (notice we kept the units the same)

Another slightly trickier problem might ask us to find the area of a circle given either the radius, diameter or circumference of a circle. Area is a measurement of flat, two-dimensional space or in other words how much space on the ground will this circle take up. The formula we will always use for this type of problem is Pi(r)^2 or Pi times r squared.

If we are given the radius, say a radius of 13 kilometers then we simply plug this into the formula and get

3.14(13 Km)^2=Area or

Area=530.66 Km squared (note; area is always expressed as units squared, this refers to the two dimensions we are working with)

If we are given the Diameter then we must simply divide the length of the diameter by two and then proceed with our formula. Same we are given a Diameter=13.23...hands?. Divide this by two to find the radius and you will get r=6.615 hands. Now plug this into the formula and get the area.

3.14(6.615)^2=Area or

Area=137.4 hands squared

Lastly, if we are given the circumference we can use some simple algebrausing the formula from the first problem to find the radius and then solve using the formula presented in the last two examples examples above to find the area. Let's same we are given the circumference of 55.34 In. and asked to find the area of the circle.

First we take the formula C=Pi(D) and plug in our numbers to get;

55.34=3.14(D) divide both sides by 3.14 leaving D=17.6242. Now cut this diameter in half to get our radius, 17.6242/2=8.812. Now plug this into our formula for area of a circle.



A=243.83 In. squared


    0 of 8192 characters used
    Post Comment

    No comments yet.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)