# Looking for segment of circ formula **URL:** \ **Category:** Factual Questions\ **Created:** [October 16, 2013, 8:42pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433 "2013-10-16T20:42:27Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [October 16, 2013, 8:42pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/1 "2013-10-16T20:42:27Z")
Suppose I have an archway, I know the width and the height of the arch. I know how to find the radius but I don’t know how to find what portion of the circumference my arch is? ---
**Author:** ![Simplicio](https://avatars.discourse-cdn.com/v4/letter/s/c37758/32.png) [@Simplicio](https://boards.straightdope.com/u/Simplicio)\ **Post date:** [October 16, 2013, 8:46pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/2 "2013-10-16T20:46:15Z")
Width divided by the diameter gives you the sin of the central angle. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [October 16, 2013, 8:48pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/3 "2013-10-16T20:48:35Z")
> [@HoneyBadgerDC](#): > > Suppose I have an archway, I know the width and the height of the arch. I know how to find the radius but I don’t know how to find what portion of the circumference my arch is? If I’m picturing this right, the angle of the arch is 2 times the arcsine of half the width divided by the radius. The portion of the circumference is that angle divided by 2 pi. ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [October 16, 2013, 9:06pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/4 "2013-10-16T21:06:06Z")
I will have to study up on sin but I think I can get it from here. I wish I would have stayed in school a bit longer I never thought I would need this stuff. ---
**Author:** ![Kyrie\_Eleison](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kyrie_eleison/32/7682_2.png) [@Kyrie\_Eleison](https://boards.straightdope.com/u/Kyrie_Eleison)\ **Post date:** [October 16, 2013, 9:14pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/5 "2013-10-16T21:14:25Z")
By portion of the circumference, do you mean the angle subtended? Law of cosines: cos[sup]-1[/sup] (1 - w[sup]2[/sup]/2r[sup]2[/sup]) On preview, I think **Andy L** calculated the same thing using half the subtended angle instead while I was searching for the vbulletin code for superscript. ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [October 16, 2013, 9:39pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/6 "2013-10-16T21:39:49Z")
What I am doing is some illustrations of bows and arrows. I know from experience that If I use a string 3" shorter than the bow I will get a braced height of about 6". I want to be a bit more precise in my illustrations as I will be using quite a few different radiuses. ``` So by portion of the circle I mean if I know the width and height I also want to know the exact length of the portion that is arched. ``` ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 16, 2013, 9:59pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/7 "2013-10-16T21:59:07Z")
I don’t know if this is a concern for you, but the shape of a bow is not generally an arc of a circle. ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [October 16, 2013, 10:19pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/8 "2013-10-16T22:19:54Z")
> [@Chronos](#): > > I don’t know if this is a concern for you, but the shape of a bow is not generally an arc of a circle. I will actually be working with portions of the limb that are bending in a radius. The english long bow is often tillered to bend in a smooth continuous arc, But I primarily work with stiff handled bows that do not. The particular thing that I will be demonstrating can be best illustrated and expalined using each limb tillered into a continuous radius. ---
**Author:** ![JM\_Hanes](https://avatars.discourse-cdn.com/v4/letter/j/6a8cbe/32.png) [@JM\_Hanes](https://boards.straightdope.com/u/JM_Hanes)\ **Post date:** [October 16, 2013, 11:15pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/9 "2013-10-16T23:15:29Z")
As I understand it, you are looking for a calculation which will give you the length, presumably in inches, of your curved material? I’m not sure I know the technically precise way to write out the following equation (corrections welcome), but when I was attempting to determine the length of a curved landscape wall in linear feet, my surveyor gave me this formula: [(°degree of angle x pi)÷180] x Radius That would be the angle at which your two radii converge, and it presumes you have fixed points at which your curve begins and ends. For all I know, this may be the same thing someone more mathematically savvy has already suggested above – or may solve a different problem from the one you’re trying to work out! Thought I’d just throw it into the pot, on the off chance that it’s what you’ve been looking for. ---
**Author:** ![sylmar](https://avatars.discourse-cdn.com/v4/letter/s/b782af/32.png) [@sylmar](https://boards.straightdope.com/u/sylmar)\ **Post date:** [October 17, 2013, 1:38am UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/10 "2013-10-17T01:38:10Z")
> [@HoneyBadgerDC](#): > > _ **I will have to study up on sin** _ but I think I can get it from here. I wish I would have stayed in school a bit longer I never thought I would need this stuff. A lot of folks I know go to Vegas for advanced studies, but I’ve always felt it’s better to develop a sense of community by supporting home grown graft and vice… ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [October 17, 2013, 1:42am UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/11 "2013-10-17T01:42:32Z")
This page has helpful illustrations [Circular segment - Wikipedia](http://en.wikipedia.org/wiki/Circular_segment) ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [October 17, 2013, 2:38am UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/12 "2013-10-17T02:38:19Z")
> [@Andy\_L](#): > > This page has helpful illustrations [Circular segment - Wikipedia](http://en.wikipedia.org/wiki/Circular_segment) That really was helpful, gave me a better grasp on what I am looking at. My math stopped at arithmatic so anything with letters or symbols I have to research a bit to figure them out. ---
**Author:** ![bump](https://avatars.discourse-cdn.com/v4/letter/b/7c8e57/32.png) [@bump](https://boards.straightdope.com/u/bump)\ **Post date:** [October 17, 2013, 1:31pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/13 "2013-10-17T13:31:23Z")
> [@HoneyBadgerDC](#): > > My math stopped at arithmatic so anything with letters or symbols I have to research a bit to figure them out. Not to be rude, but how did that happen? I thought everyone was required to take algebra (a couple of years worth), trigonometry (what your question is), and geometry at a bare minimum to graduate from high school. We did anyway, with the added fun of a semester of computer programming and a year of pre-calculus, which is basically where algebra and trigonometry are combined without using derivatives or integrals. ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [October 17, 2013, 2:39pm UTC](https://boards.straightdope.com/t/looking-for-segment-of-circ-formula/671433/14 "2013-10-17T14:39:29Z")
I got a little taste of alegebra in the 8th grade but my lifestyle changed right about that point and my education pretty much came to an end. I was using the Khan academy online to advance my math skills but the problem I had with that was nothing seemed to stick for than a few days. I advanced really rapidly by following the direction and taking the tests but I found without some practical applicatian or a lot more practice I just retained all most nothing. ``` Once I saw the diagrams of how it was figured out I knew immediately how to do it but I did not know what sine, cosine, or the other symbols actually meant, I only had some idea what they meant. I went to high school in the 60's. I never carried a single book to a single class or did a single homework assignment and still somehow managed to graduate. I went to night school for the goverment and history classes I had to make up. ```