How To Calculate Sides Of Octagon For Building Foundation - Construction Math

www.homebuildin... Click on this link for more helpful videos about building foundations, new house construction and home repairs. This video will provide you with what I would consider to be the simplest way to calculate the sides of an octagon for practically everything you're going to do with this geometric shape in the construction industry. Another video for carpenters and do-it-yourselfers about keeping things as simple as possible.

[@tebger]

Here’s how I learned, it’s simple and works. 147” multiplied by 5 divided by 12 = 61-1/4” length of side. Learned this 40 years ago from an old carpenter who got it from a really old book. It has always worked just fine whether it was a foundation or furniture. For an octagagon with a 4 ft Square- 48 inches times 5 divided by 12 equals 20” point to point.

[@gregvancom]

Your method works, it's just not as accurate or accurate all the time. I tried a few formulas before using this one.

[@brankomarkovina4061]

I have been trying to work this out for years, and you made it so easy. THANK YOU.? X 5 ÷ I2 .if you were in Australia I'd bye you a beer 🍺 😉 🤣

[@tebger]

@@gregvancom Quick, simple and accurate but think and do whatever you want.

[@signmeupruss]

I build octagonal structures all the time and for the level of quality I want, the difference between 61.25 and 60.88 is far too big a discrepancy. If I want the 8 sides to fit within the 147 inch square, the sides on the diagonals would only be 60-5/8", a full 5/8" off. For your 48 inch example, an octagon inside the 48 inch square would have sides of 19 7/8", not 20. If the sides of the octagon which are along the sides of the 48 inch square are 20 inches, then the sides on the diagonals are only about 19 3/4" For me, it's better to remember that the factor for determining the length of a side of an octagon(having all 8 sides the same) within a square is the square root of 2 minus 1, which is 1.41421 - 1 = 0.41421, the same factor Greg cites in the video. I prefer the 0.41421 because it allows me to set a stop for my saws and make all the sides the same length, and have it fit perfectly within the desired footprint. Greg's factor(0.41421) derives from the fact that the length of a side of the square, call it W, equals the one length of an octagon side, call it S, plus 2 times the length of a side divided by the square root of 2. So, W = S + 2(S/sqrt(2)) . After simplifying, W = 2.41421 S and solving for S, we get S = 0.41421W. This reveals the factor Greg used.

[@timwelch175]

Having this knowledge is priceless. Thank you sir.

[@shaneennest9176]

Hey Greg! I'm a shop teacher and just used this to help a student make an octagonal table top. Thank you! I also teach applied math so I'm going to show your video in math class this afternoon. Regardless of the tan22.5(degrees) or square root of 2-1, this method works. I'll try to piece together the why part but results count and you bucked down when it was needed - CHEERS mate!! I'm super grateful!!

[@gregvancom]

Awesome.

[@treich1234]

Your videos are worth every minute of their run time...Period

[@gregvancom]

Wow, I always enjoy hearing comments like yours. Thanks for watching and taking the time to let us know how much you like our channel.

[@mbernica224]

By far the best and easiest way to create an octagon that I have seen. Well done.

[@sizwe.amabaso732]

As soon as u started using feet and inches I zoned out

[@virginiarayn5939]

It's like time traveling back to high school.

[@darcy2965]

Haha

[@smraish2342]

😀

[@salihudintaiwo4205]

It's not hard to remember 254mm/2.5cm is an inch, 12'' make a ft. 3.33ft/3'4" = 1metre 10ft is 3m, 12'3" is 3.75m

[@danmcdonagh8924]

Oilers did all of that on my own just recently. The building I'm going to do is 10'x10' times that magic #. It was very easy to get and mark out all .measurements

[@jasonm887]

This checks out. Perfectly square octagon. Ty!

[@gregvancom]

Awesome

[@mikebraddee4880]

That's exactly how I have been doing it for years. simple math. Nice job.

[@gregvancom]

Cool, thanks!

[@victortoro8728]

thank you i was over thinking it

[@ajsironworks3937]

Thankyou sir. I’m a welder and I wanted to know how to find the length of the sides of the octagon fire pit I was building. It goes out from 3 feet at the bottom to 4 feet at the top glaring out. But the putter ring was messing with me and we got it figured out but I knew there had to be an easier way. Thankyou so much. Appreciate the talking and explaining.

[@gregvancom]

You're welcome and thanks for taking the time to let us know. Comments like yours are always sincerely appreciated.

[@baldwelder8775]

me too, i have to make a cover for a well, for the boss and the onus is on me to make if secure to protect his precious grandkids. It`s 36" diameter and I have to make it out of angle and I have to weld some more angle inside to support a grid.... the worst is, I have to make it from a length of angle and the support needs welding on 1st, and the saw only cuts to the one side 🥵

[@terrybullock3140]

I actually watched this after failing to be convinced by some other videos. My application was slightly different in that I just wanted to turn a square-section post into the largest possible regular octagon. In this case (which matches your numbers), you'd just have your table saw blade at 45° and set the fence xx away from it, where xx is half the diagonal measurement of the post. Run the post through four times (obvs), and each face will be 0.41421 of the original face.

[@gregvancom]

Thanks for sharing and that's a good way to build angles off a square foundation.

[@jonathonlyles3349]

❤ the video absolutely helped me out making a table

[@gregvancom]

Fantastic!

[@G4zzzzz]

Thank you. I have always loved math but am plagued with dyslexia. Thus have worked most my life as a therapist, artist, handyman. Where did you get the magic number?

[@gregvancom]

I think I put the information in one of our videos in the comment section.

[@murphy2823]

Thank you. This is very useful.

[@gregvancom]

Glad it was helpful!

[@epictrundling4639]

I think you started the video without stating what size octagonal gazebo you were planning - or did I miss it? Thx!

[@00Luvofficialpage]

hey hows it going. Just to double check. if i was going to be working with a requested 20ft gazebo would i just convert that to inches then use your calculations for the foundation and setting up the eight sides? Thanks so much for any help. simple questions that I will not be overthinking thanks to ya.

[@jerrymapes9745]

In this example is the 147 inches to the inside or outside of the square?

[@gregvancom]

Inside and sorry I didn't make it clear.

[@user-kp5mp1tz5k]

thanks a lot

[@criscrouse4343]

Take the width measurement and multiply it by .4142135

[@Elrod831.]

So when you cut the pieces for the octagon, the number 43 1/16 where is that transferred to

[@WayneCroney]

Thank you

[@gregvancom]

You're welcome

[@stone9485]

Ooookay, so if I need to end up with a ten foot octagon, each side ten foot, then how do I do it? Maybe I ma just tired or dumb. thanks

[@johnblyth9787]

Divide length of sides of square by 3 and multiply by 1.24 = sides of hexagon

[@Jay-tk7ib]

Great video.

[@richardrichard5409]

brilliant sir!

[@ojmorals1]

hey Greg, how did you come up with the .41421???? im gonna try to see if this works but i want to know where this number came from.... thank you..

[@gregvancom]

I don't know, but I did a lot of research and worked a lot of calculations before making the video to provide the viewers with what I believe to be the simplest and most effective formula. There were a few that worked on smaller octagon's, but didn't work on larger ones.

[@peterbell4154]

Hi .41421 is the Tangent of 22.5 degrees.

[@thesuperjacobshow8151]

The number comes from the square root of two minus 1.

[@jeffreykountz3743]

Wow and I spent all day trying to figure this out my boss the engineer trying to help me....you explained it very simple. Got one question where how did you get .41421

[@signmeupruss]

It's useful to note that if you multiply the 43.05, the length needed to center an octagon side on the square, by the sqrt 2, you will get 43.05 X 1.41421 = 60.88.

[@dougstewart3546]

Another Great Video. Thank you, Greg!

[@gregvancom]

Glad you liked it and even more glad you didn't find anything wrong with it :)

[@dougstewart3546]

@@gregvancom You must know, that was exactly my fear with the other video! Keep doing what you're doing! The best on the Internet! (And I apologise foe any previous hurtful comments.)

[@leexgabriel]

Thank you sir

[@jeffneale1457]

Thank you. You just made me some money.

[@gregvancom]

Great!

[@majorhellrazor4054]

I'd just took half the diagonal and pulled that from each corner to get my marks.. 147 x .414 to make sure my lengths are correct

[@gregvancom]

I just tried it and it didn't seem to work, feel free to provide us with a better explanation.

[@scottsavoy9627]

The length of the side minus the half length of the diagonal equals the distance from the corner.

[@Wordzwurth]

1. Determine desired side length (long point to long point) 2. Cut all sides to desired length with a 22.5 degree angle. 3. Assemble all eight sides at the corners and check all corner to corner distances are equal(check for square). No calculator or math needed! Th "magic number" is 22.5 degrees!! Math suckes!! I avoid it whenever possible!!! This video has made me sleepy 😝

[@hippiehillape]

TAN(22.5°)

[@BrickandBlockWork]

So is .41423 also applicable even when you using cm ?

[@gregvancom]

Yes, I just converted the measurements to centimeters and it worked.

[@erlingormar]

2:50

[@OffGridGetAway]

Could have used this a couple years ago when we built our hogan.

[@LJTomlinson1]

How do I work this problem in reverse? . I want to make the sides of my Hogan 15 ft or 180 inches per side for a 1200 sq ft Hogan

[@gregvancom]

See if this helps. kzbin.info/www/bejne/rXTQdaaBqsmMbKM

[@ChristopheDJediRonin]

Thanks a lot ☀️💖☀️!!!

[@gregvancom]

You are so welcome

[@mfahadaziz5461]

very nice video . sir how did you got the .41421 number ? I want to make a gazebo of 7x7 so should I go with 7.3 x 7.3/

[@gregvancom]

I found the number while searching for the easiest method to figure something like this out, so won't be much help figuring out where it came from. If the outside dimensions are going to be 7' x 7', then start with that. I don't think this answered your question, but feel free to provide me with more details if it didn't.

[@billf7062]

The boards that are cut form a hypotenuse (the cut is a 45 degree cut on both ends) and merge into the straight board(s). In the video, the cut is 45 degrees, the INSIDE angle that results is 135 degrees (180 - 45 = 135). The OUTSIDE of the 135 degree angle is 45 degrees (2 miters 22.5 degrees) 22.5 Tangent = .41421 Working backwards, this number multiplied by one side of the square in inches e.g. 147”(.41421) = 60.88 provides the hypotenuse portion within the square.

[@thesuperjacobshow8151]

The 0.4142 is the sqare root of 2 minus 1. The square root of two is the ratio of the width of an octagon to the sides. So you take the total width, then subtract double the width divided by the square root of two. Which the same as multiplying by the square root of 2 minus 1. Which approximately is the same as multiplying by 0.4142.

[@luiselizalde6757]

Excellent thanks

[@gregvancom]

Glad you liked it.

[@Unholcannoli760]

what does the .41421 represent? thanks for the knowledge

[@gregvancom]

I don't know, but I did do a lot of research and tried to find the easiest way and it was all about using this number. If anyone knows what this number is then I would love to know also.

[@scottsavoy9627]

It's the tangent of 22.5 degrees.

[@valkasolidor6727]

@@scottsavoy9627 I built a little octagonal workshop out back years ago and had a heck of a time finding useful instruction. I did manage to work out this angle though, meaning of course that my corners would be 67.5 degrees.

[@melnez1512]

This is great! How many inches in diameter is best for desired length diameter closest to 40' or 480" diameter octagon? What diameter closest to 40' or 480" is best for standard construction of an octagon house?

[@gregvancom]

The video will help with figuring out what you need and email me a design of your house and I will put it on my list of videos to be made in the future.

[@royalmashonte2091]

Hell yeah. Thanks.

[@gregvancom]

Glad you liked it and you're welcome.

[@BallawdeQuincewold]

I don't really follow this at all. Why not just derive it? Let X be the octagon side length. Let A be the side length of those 4 right triangles Let L1 be the length of the shorter side Let L2 be the length of the longer side X = sqrt(A^2 + A^2) L1 = X + 2*A L2 = L1 + 2*board width (where board width is 3" for 2x4) Plug and chug. I'm not a carpenter but this seems way simpler than remembering magic numbers. Am I wrong?

[@gregvancom]

No, if this seems easier, then use it.

[@hudsonsoul1121]

Octagon lengths = span(1800) - 58.6% Example 1800 span -58.6% 1054.8 =745.2

[@gregvancom]

I tried it and it didn't work. I used your formula, but my software showed 689 units for the sides with an 1800 unit span.

[@hudsonsoul1121]

gregvancom strange because l use it regularly and it's never failed me. I've not tried your method, have you cut those lengths at 689 and mitred at 22 1/2 degrees?

[@gregvancom]

@@hudsonsoul1121 I got it working. My mistake was that I took the span measurement form opposing points or from one corner of the octagon to the one on the other side instead of measuring the span from side to side. It works great and I will try to make another video with your method in hopes other will find it easier. Thanks.

[@hudsonsoul1121]

gregvancom wonderful news, l did wonder if you made a mistake because I knew it's worked well for me. All the best with the new video.

[@billsmith9249]

Nice video but unfortunately did not help me with my project. :( I am building an in ground fire pit, and the 'ring' is actually an octagon made out of cinder blocks. I got the 'rough' form together before I started digging, but now that I have the paver material down, it is time to set the cinder blocks. I cannot for the life of me to get everything in square. :(

[@thurainlinnnaung726]

Dimensions is 12'-3"x12"-3" right?

[@gregvancom]

Yes, 12 feet three inches square in example.

[@rolandthethompsongunner64]

I have to place posts in a hexagon pattern to build a rustic structure and having a difficult time figuring where my posts will be to maintain a consistent 20’ space. I figured it would be easy. It isn’t. How ancient man figured this out is mind boggling. So is an octagon easier to construct than a hexagon ? With the hexagon everything I’ve found in regards to laying it out involves a circle and using pie to calculate where your 6 points will be. But every time I try and draw it out on paper the distances change in regards to my desired 20’ area 10’ of separation of posts. I figured 10’s and 5’s would be nice numbers to work with. But I’m struggling.

[@gregvancom]

Email me a drawing with your measurements.

[@signmeupruss]

From Greg's formula, the side length of the octagon equals 0.41421 times the side of the square. If the square width is W and octagon side is S, then the formula is S=0.41421 X W. But, that also means that W = S / 0.41421. So, if you want S to be 10 feet, then the square will have a width of 10 / 0.41421 = 24.1423 feet(about 24 ft 1 11/16 inches). If you want your octagon to fit within a square having sides of 20 feet, then your octagon side would be 20 ft X 0.41421 = 8.2842 ft(8 ft 3 7/16 inches).

[@metparker]

Your boards are not laid out correctly. Your side boards are located inside the top and bottom boards making the length of the sides is the length of the side boards plus the thickness of the top and bottom boards.

[@DerekTJ]

It's a good video 😝

[@gregvancom]

Thanks 😅

[@jimwest4060]

Where did •41421 come from?

[@gregvancom]

I think there's an explanation in the comment area.

[@Minhaahmedawan10]

But how did you get the 0.41421?

[@gregvancom]

I found it will doing research for this video.

[@herbsu4330]

Length of sides, inside or outside dimension?

[@gregvancom]

In the video it would be the outside of concrete foundation and inside of building forms.

[@herbsu4330]

@@gregvancom I realized thatfurther into the video.

[@parepidemosproductions4741]

I know how you got .41421... but why that and not 1.4121 (which is the sqrt of 2, which I'm guessing is how you're choosing the length of our octogon)

[@gregvancom]

So that number comes from the square root of two. Now if you're not kidding and simply made a mistake in your math, why would we use the number you're suggesting.

[@parepidemosproductions4741]

@@gregvancom idk!😅 For some reason I got without 1 the first time 🙃😂😂😂 just double checked now, thanks 💯

[@johnforeman9926]

How did you get that "magic number"...you didn't explain that. Most construction teachers forget that also!

[@gregvancom]

Yes, bad teacher... I didn't create the magic number, so won't be able to provide you with that information. I found at least three methods you could use on the Internet, but they weren't accurate, but this one seemed to provide excellent results.

[@peterbell4154]

Hi Tangent of 22.5 degrees is 0.4142

[@alexmathew6786]

Quantity of concrete for this foundation

[@gregvancom]

I will try to make a video in the future to provide viewers with a way.

[@manis7252]

Yeah right

[@djstl100]

Divide width of one side by 2.41 ...you have all 8 lengths, don't know why people make it so hard..

[@gregvancom]

Can you provide us with an example of your math or walk us through it. I've found that some of the simple methods don't provide accurate results. Help us make it easier if you can.

[@hudsonsoul1121]

Octagon lengths = span(1800) - 58.6% Example 1800 span -58.6% 1054.8 =745.2 This method works because the measurement of a square corner to the centre measurement can determine your point of which your 45degee angle side starts. Half of 58.6 is 29.3 which is the measurement from the corner of the square towards the middle.

[@darcy2965]

How to do it if I don't want to make the square, just the octagon. I got the math ok 👌

[@gregvancom]

I will put your video suggestion on my list.

[@thesuperjacobshow8151]

Each edge of the octagon is equal to to the width of the octagon minus the width of the octagon multiplied by two and divided by two plus the square root of two. X = length of an edge Y = Width of the octagon X = Y - (2Y)/(2+√2)

[@charlesjones7922]

to get the exact length of a side of an octagon multply five twelveths times the diameter your measurements is short the correct length is 61.25 to check yourself multiply 61.25 by 12 it equals 735 divide that by 5 it equals 147 my way is the easiest way amen

[@gregvancom]

I tried a few different ways and some of them didn't provide me with good results and if you're suggesting that my numbers are wrong, when they were drawn in one of the most awesome computer-aided design software programs, then who am I to argue.