# Is there an easy formula the calculate the floor area of a geodesic dome structure?

**URL:** <https://boards.straightdope.com/t/is-there-an-easy-formula-the-calculate-the-floor-area-of-a-geodesic-dome-structure/369894>\
**Category:** Factual Questions\
**Created:** [August 23, 2006, 3:46pm UTC](https://boards.straightdope.com/t/is-there-an-easy-formula-the-calculate-the-floor-area-of-a-geodesic-dome-structure/369894 "2006-08-23T15:46:34Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\
**Post date:** [August 23, 2006, 3:46pm UTC](https://boards.straightdope.com/t/is-there-an-easy-formula-the-calculate-the-floor-area-of-a-geodesic-dome-structure/369894/1 "2006-08-23T15:46:34Z")

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One of my fellow commercial real estate agents has a property for sale that contains a geodesic dome structure. Is there a relatively straightforward way to calculate the floor area?

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**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\
**Post date:** [August 23, 2006, 3:56pm UTC](https://boards.straightdope.com/t/is-there-an-easy-formula-the-calculate-the-floor-area-of-a-geodesic-dome-structure/369894/2 "2006-08-23T15:56:02Z")

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Yes. Yes there is.

Area=3.14159 \* radius^2.

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**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\
**Post date:** [August 23, 2006, 4:35pm UTC](https://boards.straightdope.com/t/is-there-an-easy-formula-the-calculate-the-floor-area-of-a-geodesic-dome-structure/369894/3 "2006-08-23T16:35:44Z")

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Or, since it’s easier to measure the distance across the building, the diameter, you can use:

area = distance across[sup]2[/sup]\*22/28

On a 40 ft. building you will be off by 1/2 ft. sq. from using the true value of π

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**Author:** ![633squadron](https://avatars.discourse-cdn.com/v4/letter/6/ee59a6/32.png) [@633squadron](https://boards.straightdope.com/u/633squadron)\
**Post date:** [August 23, 2006, 4:38pm UTC](https://boards.straightdope.com/t/is-there-an-easy-formula-the-calculate-the-floor-area-of-a-geodesic-dome-structure/369894/4 "2006-08-23T16:38:46Z")

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> [@Lemur866](#):
>
> Yes. Yes there is.
> 
> Area=3.14159 \* radius^2.

That is, geodesic domes are approximations of spheres. The ideal dome uses flexible support members that form geodesics (“great circles”). Therefore, when constructed they form a sphere. The intersection of a plane that is perpendicular to the sphere’s radius and bisects the sphere is a circle, so the floor area is the area of a circle (pi times radius squared).

**However** , this neglects the reality of geodesic domes in construction. Very few of them are “perfect” spheres. I have built model geodesics that use pentagons; others use alternating regular polygons as components. So using the area of a circle is just an approximation.

By the way, a geodesic is a an arc on the circle formed when a plane intersects a sphere and contains the sphere’s center. Another way of looking at it is that a geodesic is the shortest distance between any two points on a sphere.

The most common everyday occurrence of great circles is airplane routes, especially between continents.