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Discussion Starter · #1 ·
First of all, I don’t post much but I have gleaned much from reading here. But I haven’t been able to find my answer to this question.

I have three different radiuses that I am trying to find without using the “guess” method. I don’t have a true diameter for any of these radiuses. I found a radius calculator that allows me to put in the width and a height and it’ll give me a decimal radius but I’m having a hard time converting it to a usable measured fraction.

Typically, I’d get my width (19’), find center and then measure up to my height (3’-6”), snap a right angled cross on the floor and then start measuring down until I got my arch to cross both points - guessing.

So with my example, my arch is 19’ across and it’s 3’-6” high. The radius calculator says my radius is 14.642857142857142. How can I convert this into something I can use? I don’t have measurements for the other two. I am routing top trim pieces for all these.

Thanks in advance.
 

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...looks like it's 14' 7 11/16"...
 

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Discussion Starter · #3 ·
Thanks Nick! Would you care to share how you got that? I’ll need the info to find my other two radiuses.
 

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Thanks Nick! Would you care to share how you got that? I’ll need the info to find my other two radiuses.

...multiply everything to the right of the decimal point by 12...that will actually give you 7 5/7" but rounding to 16ths will make it 11/16ths...
 

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So really, your question is decimal to fractional with feet/inches thrown in for good measure? In this case you have a 14 and .6428 feet as a radius (ignore the rest of the fraction). Multiply the fractional part by 12 for 7.7136". So 14' 7.7136". To get the fractional inch (.7136), you do the same but with 16 instead of 12 for 11/16" ( .7136/16 - 11.4176), though I would just use 3/4" So, 14' 7 3/4"

I guess this is where the metric boys rightly explain how screwed up the imperial system is. I wouldn't argue that point but it is an extreme case.

[edit] I see nick beat me to it while I was composing. by the way, the difference between 11/16 and 3/4 is .02%.
 

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Depends on whether you're working with a true circle, or an arc. A circle is pretty easy, infact, here's a calculator where you put in the number for the radius in inches, and it calculates the rest. https://www.omnicalculator.com/math/circumference

If you are calculating an arc, you are only using a portion of the circumference, and it is more complicated. I found this calculator and explanation that may help. It is high school math, but I sure as heck don't recall this. https://handymath.com/cgi-bin/arc18.cgi?submit=Entry

Hope this is helpful.
 

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Discussion Starter · #7 ·
Thanks much guys! That’s what I wanted to learn! So when I come up with decimals, if feet is my whole number, I multiply the decimal by 12 to get it to inches. Then I can multiply the remaining decimal by 8, 16 or 32 depending how far I want to break it down (8ths and 16ths is typically good enough). This will be my first (2nd and 3rd) large radius to rout. I’m looking forward to it but want it to be perfect.
 

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Convert it to metric. Easy peasy then. No fractions. Your answer will be accurate to 1/25th of an inch.
 

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Thanks much guys! That’s what I wanted to learn! So when I come up with decimals, if feet is my whole number, I multiply the decimal by 12 to get it to inches. Then I can multiply the remaining decimal by 8, 16 or 32 depending how far I want to break it down (8ths and 16ths is typically good enough). This will be my first (2nd and 3rd) large radius to rout. I’m looking forward to it but want it to be perfect.

Exactly...whatever you want the denominator of the fraction to be...

Have fun...
 

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Discussion Starter · #10 ·
@desertTom

This would be an arc because it’s just the top part of a circle. If I had the diameter then the radius is half the diameter. I’m not sure the formula used to get the arc but the arc calculator does the work.

I don’t recall much high school math either. I tried to forget as much as I could and then later realized I need some it.
 

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@desertTom

This would be an arc because it’s just the top part of a circle. If I had the diameter then the radius is half the diameter. I’m not sure the formula used to get the arc but the arc calculator does the work.

I don’t recall much high school math either. I tried to forget as much as I could and then later realized I need some it.

:grin:...isn't it interesting how we only now realize we shudda listened to da teach...:grin:
 

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Another possibility that I use from time to time, is to use a good 1 meter rule that has inches on one edge and and metric on the other. Measure in metric (I have a metric/imperial tape measure for larger items). Cut the number in half (divide by 2), then using a small T or L square to line up on the metric measure and you look to the opposite imperial number. But simply using metric would be far easier, it's just that I have trouble visualizing in metric because of decades of forming Imperial visualizations. Deeply imbedded habit is a simpler word for it.

I usually do a rough drawing of a project on 1/4 inch 11x17 pads. I can adjust the scale by the full size dimension I ascribe to each square. Laying out a room, for example, the scale was 1/4 inch = 3ft.

For smaller projects, it would likely be easier to work in metric, using a smaller grid in metric units of 10 to do the design. The only slight problem occurs when using Imperial tools to cut metric measures, but even then (Dados for example), you could measure the stack thickness with a metric rule. If using 18mm BB ply, you have to adjust to the slight difference anyhow.

Good post, got me thinking a little out of my Imperial box. I think I need to consider getting a better quality metric tape measure. At least we're not working in cubits anymore.
 

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Thanks much guys! That’s what I wanted to learn! So when I come up with decimals, if feet is my whole number, I multiply the decimal by 12 to get it to inches. Then I can multiply the remaining decimal by 8, 16 or 32 depending how far I want to break it down (8ths and 16ths is typically good enough). This will be my first (2nd and 3rd) large radius to rout. I’m looking forward to it but want it to be perfect.
Yup, you got it! It's kind of annoying that the imperial system uses multiples of 10, 12 and then powers of 2. I guess when you have yards you gotta toss in multiples of 3. yuck. Metric IS easier but you still have to deal with feet/inches/yards in the good ole USA.
 

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Discussion Starter · #15 ·
I spent most of the day cutting radiuses, 5” with a 3” on top and 6” with a 4” on top. This place is full of radiuses and they want them all trimmed. Finding and calculating the radiuses was easy thanks to the info gleaned from this thread. I have 2 more radiuses to cut tomorrow and then the trim pieces to cover those. I’d like to have all radiuses (and their trim) cut by the end of tomorrow. Then I can build and trim Thursday and Friday.
 

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First of all, I don’t post much but I have gleaned much from reading here. But I haven’t been able to find my answer to this question.

I have three different radiuses that I am trying to find without using the “guess” method. I don’t have a true diameter for any of these radiuses. I found a radius calculator that allows me to put in the width and a height and it’ll give me a decimal radius but I’m having a hard time converting it to a usable measured fraction.

Typically, I’d get my width (19’), find center and then measure up to my height (3’-6”), snap a right angled cross on the floor and then start measuring down until I got my arch to cross both points - guessing.

So with my example, my arch is 19’ across and it’s 3’-6” high. The radius calculator says my radius is 14.642857142857142. How can I convert this into something I can use? I don’t have measurements for the other two. I am routing top trim pieces for all these.

Thanks in advance.

Just had a read of this post and looked for a simple possible solutions.


With what tool are you going to cut the arch?


Could you just use a flexible stick between 3 nails?
 

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Discussion Starter · #17 ·
Just had a read of this post and looked for a simple possible solutions.


With what tool are you going to cut the arch?


Could you just use a flexible stick between 3 nails?
I used my Dewalt plunge router to cut all my radiuses. My largest radius was 19’-11”. I shot a 2x6 to the floor and screwed 3 1x4x8s together to get the distance I needed. I secured my radius point to the 2x6 and the 1x4s to my modified router base. I made 4 passes on each cut to get all the way through. No issues!
 

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Hi Mark,
Several other forum members have described how to convert a decimal measurement into a linear one already. The formula that I've used during my carpentry career is: Left x Right = Top x Bottom. (L x R=T x B) Or to find the variable (the bottom half of the circle that your arc is a part of) L x R ÷ T = B
Then add B + T for the diameter. Then divide by 2 for the radius. Think of a 16" pizza for example. If L x R = T x B then 8" x 8" = 8" x 8". That equation remains a constant within a circle as long as the two intersecting lines remain perpendicular.
In your case L= 9'-6". R=9'-6". T= 3"-6" I'm also assuming that your are using a standard calculator rather than a linear. So then L=9.5. R=9.5. T=3.5
Calculation: 9.5 x 9.5=90.25
90.25÷3.5=25.78571
25.78571+3.5=29.28571 (Dia.)
29.28571÷2=14.64286 (Radius)
End result: 14'-7 11/16"
 

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Discussion Starter · #19 ·
Hi Mark,
Several other forum members have described how to convert a decimal measurement into a linear one already. The formula that I've used during my carpentry career is: Left x Right = Top x Bottom. (L x R=T x B) Or to find the variable (the bottom half of the circle that your arc is a part of) L x R ÷ T = B
Then add B + T for the diameter. Then divide by 2 for the radius. Think of a 16" pizza for example. If L x R = T x B then 8" x 8" = 8" x 8". That equation remains a constant within a circle as long as the two intersecting lines remain perpendicular.
In your case L= 9'-6". R=9'-6". T= 3"-6" I'm also assuming that your are using a standard calculator rather than a linear. So then L=9.5. R=9.5. T=3.5
Calculation: 9.5 x 9.5=90.25
90.25÷3.5=25.78571
25.78571+3.5=29.28571 (Dia.)
29.28571÷2=14.64286 (Radius)
End result: 14'-7 11/16"
Very interesting! I’ll have to write that one down and use it. I love learning new things and this is definitely new. I’m using an online radius calculator that allows you put in the length and height and it gives you the radius. Your formula is more than likely the formula in that calculator.

Thanks for the info!
 

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Might also make it easier to round up the decimal to the nearest 10th. 14.642857142857142 would be 14.64. Anything smaller is so small that it doesn't matter in woodworking. I could be wrong here after reading the other post but I read that as 14' 3/16". Didn't read anywhere where you mentioned metric. The arc radius is the length of the radius from beginning to end.
 
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