I’ve toured a lot of historic homes and seen some extraordinary arches—door jambs, windows, passageways. In reading about historic architecture, especially Gothic and colonial styles, I’ve come across some beautiful arch work. But those once-common elements are not often incorporated into millwork today. Sure, sometimes the carpentry techniques are more difficult, and too costly, but the problem I’ve recognized is more one of design.
Combining a group of openings with segmental jambs can look awkward if the spring lines are at different elevations, if the tops of the arches vary in height, or if the spans are significantly different (see image, below, click to enlarge).
|And segmented jambs can look even worse if keystones are used improperly. Remember, you can only put a keystone in one and only one spot—at the apex of the arch (see “Parts of an Arch,” below).|
And another thing . . . segmented radius arches do not look good when they’re decorated with classical head details. Doesn’t there appear to be something missing in both of the pictures below? Yes, there is—structural support and a defined point of termination.
Certainly, there are a lot of builders and architects who aren’t reading Get Your House Right! But the real problem I found was with instructions for laying out arches—they are all terribly outdated! In fact, almost all of the information we use today has been collected and re-printed from books that were published over a century ago—illustrations filled with confusing text, multiple lines and intersections, usually with all the information compressed into one ink drawing (see image, right).
Publishing books a hundred years ago was prohibitively expensive: the cost of a single sheet of paper was so high that private letters were often written with the text running in both directions, just to save on paper. It’s no wonder book publishers never considered multiple, step-by-step illustrations.
But that’s not the case today—at least not for an e-magazine like THISisCarpentry! Now that we have paper-free publishing, it’s time to re-draw those old instructions.
The articles in this series are meant to provide a richer format for today’s “digital savvy” carpenter. There is still a fair bit of geometry involved, but fear not! All of these articles include Quick Reference Guides, or “cheat sheets” (downloadable PDFs), with step-by-step instructions for each arch layout.
Let’s get started:
An arch is a structure that spans an opening and supports weight. Arches have been around for thousands of years, and were originally constructed out of stone. During the Roman Empire the engineering of the masonry arch was perfected and its structural element defined.
Even though decorative millwork doesn’t need to provide physical strength and support, it should do so visually. You can’t fool the eye. You might not know why, but something inside you will let you know if it doesn’t look quite right (just like the start of this next sentence!). It’s just like why choosing a terminating or supporting molding can make all the difference.
Impost: The block set into a wall or uppermost part of a column or pillar, used to support an arch.
Keystone: A wedge-shaped piece at the apex of an arch that locks the structure together and allows it to bear weight. The shape of the keystone should always be related to the center point of the arc that makes up the arch.
Spring line: The line at which an arch begins—located at or above the impost.
Stilt: The elevation of the spring line above the impost.
Voussoir: A wedge-shaped piece used to make up the curved part of an arch.
Because all of the following arch types are based on the circle, let’s review the fundamentals of circular geometry.
Arc: A curved line that is part of the circumference of a circle.
Chord: A line segment joining two points of a curve.
Circumference: The distance around the perimeter of a circle.
Diameter: The distance across a circle through its center point.
Radius: The distance from the center point of a circle to its perimeter. Equal to one half of the diameter.
Point of Tangency (tangent point): The point at which the tangent touches an arc or circle.
Tangent: A line, arc, or circle that touches an arc or circle at only one point.
Determining the radius of an arc for a given span and rise can be worked out with simple geometry, but if you have a construction calculator, you can find your radius with just a few key punches.
Here are the steps (I use BuildCalc on my iPad. If you use CMPro on your iPhone/iPad or Droid, the key locations are a little different, but steps are the same!):
Finding the radius of a segmented arch
This function of a construction calculator can also be used if you need to find the radius of an existing inside curve.
1. Cut a straight piece of wood to a length that will fit inside the arch, and touch two points of its curve. The actual length of the stick is not important, but using a nice round number like 12 in. or 24 in. will make things easier. After cutting, measure and mark the midpoint along its length.
2. Place the piece of wood against the arch—it doesn’t matter where.
3. Measure the distance at a right angle from the top of the stick’s midpoint to the existing curve.
4. Enter that measurement into the calculator and press RISE.
5. Enter the length of the stick and press RUN.
6. Press the CONV key to change the ARC key to the RADIUS key.
7. Press the RADIUS Key.
For readers who don’t have a construction calculator, here is the formula you can use with a standard calculator. Unfortunately, you also have to convert any fractions to decimals.
|Download the Quick Reference Guide for Segmental Arches
While Roman architecture is known for one-centered arches, two-centered arches are fundamental to Gothic architecture and form the simplest “pointed” arches.
|The large main parlor window at Lyndhurst is framed by a two-centered arch.|
|The lancet windows surrounding this tower are typical two-centered arches. The same motif repeats itself in a crenelated pattern across the porte cochere parapet walls. (Sells Mansion, Columbus Ohio)|
There are many variations of two-centered arches, and each depends on the location of the center points. When the center points are located closer to the middle of the span, the arch flattens out; if the center points are located farther away from the middle of the span, the arch becomes sharper.
|The drop-arch on this fireplace, beneath a suspended hood, provides just the right amount of gothic flavor for an early 20th century arts-and-crafts home. (www.adamsonhouse.org)|
The following Quick Reference Guide provides step-by-step procedures for finding the required arc centers and appropriate radii for a two-centered arch that must meet a specific height and width.
|Download the Quick Reference Guide for 2-Centered Arches
Note: A recurring step found in these geometric constructions is to draw a line perpendicular to another line’s midpoint. For simplicity, a square has been used in the illustrations, but the task can also be accomplished with just a compass/trammel and a straight edge, as shown in the following Quick Reference Guide.
|Download the Quick Reference Guide for Bisecting a Line
Don’t miss the next article in this series on Three-Centered arches, where the geometry gets a little more complicated.
Wow! Great article. Nice pictures, videos and text.
90% of the arches I see out there bug the crap out of me. The worst offender is semicircular windows that NEVER have the arch stilted.
Never knew how mixing arch types really doesn’t work.
Thanks so much.
Great article! This is the stuff I love to read! So many times someone has a set of prints with all the drawings on them, or has already ordered a door or window and you are just stuck making templates and fabricating mouldings for arches that really don’t work together and you are left scratching your head wondering where alot of these designers and architects get their training.
We often tell our clients that just because you can’t tell what it is that is wrong, doesn’t mean it’s right! You can’t fool the eyes!
Fantastic job writing this article, great pics, vids and explanations. Can’t wait for part 2!
When I read the title, I could hear the music start to play. Once I started reading, I could hear the choir sing… and that’s a tune I’d join in anytime. Great article.
I see many arches that are oval shaped on houses. Quite often arches on garage doors do not match the glass in the door.
I feel like the Double rainbow guy every time I see your Sketchup animations. This article is amazing, and I hope that everyone reading especially the ones who are doing all the built-ins with arches, are paying attention! Thank you for this timely piece, looking forward to part 2.
Double rainbow guy ” OMG OMG”
Looking forward to the continuation of this article. I see this mistake on a regular basis.
When calculating radius without the benefit of a construction calculator, I prefer to dummy things down and write it all down in a little book.. I don’t use “Rise and Run” since both words start with “R” and those terms (for stairbuilders) are already spoken for.
My little lingo and memory crutch starts with a “C” for Cord and “A” for Arrow (as in bow and arrow) with “C” being the bowstring.(I thinks me thinks better in pitchers)
C / 2 (STO) / A X (RCL) + A / 2 = Radius
Half the cord divided by the arrow, times half the cord plus the arrow, divided by two.
I’ve used this formula so often that it really ought to be engraved on my tombstone..
Anyway, very fine article and I’m looking forward to learning more about the “basket-handle arch”? (an elliptical arch that does indeed look like a basket handle) I’ve never heard that term before.
A common arch error: flexing a stick to create the curved line. This does not provide a circular arch because the stick flexes more in the center than on the ends.
Loved the first two photos, of wrongthink arches. Amazing that nobody has written this guide before. Well done!
Thank you all for the kind comments!
This project was a labor of love, and never would have been possible without the help and encouragement of Gary Katz. I would also like to thank Robert Walker, TiC’s managing editor, for his hard work and patience with me.
I hope you enjoy the next two installments and find the information useful.
Thanks for taking the time to explain and diagram this. Well done! I’m looking forward to your next article.
I’ve never run across the term “suspected hood” before. Please enlighten me.
Lots of houses have strange proportions that go way beyond the arches.
Neither have I! I think we created a new term. A suspected hood: one who enters a home and doesn’t like the arch-i-tecture. Actually, I think we meant “suspended.” :)
I like the first explanation.
A very good resource and compliment to this article is: Traditional Construction Patterns (Stephen Mouzon). I just got back from Trento and Verona, Italy and I couldn’t find any design feature out of proportion; I was in fact blown away. My wife has all these pictures of me, not window shopping or sipping fine wine, but looking up at all the buildings. Very good article and compliment to our trip.
Good article on such a beautiful feature. A downside to our manufacturing prowness is that it has become very easy to do it wrong. I suspect historically, when it was a more deliberate and costly detail it was probably more thought out in the design stage. Now folks often just pick it out of a catalog and make it fit.
I have never heard the “basket handle” term before, I like it. I look forward to the three centered arch discussion. I like the 3 centered arch over the true ellipse, particularly because it allows one to run all the profiles on a shaper with simple radius jigs- yet is comparably elegant.
Thank you for taking the time to do this article. I am looking forward to learning the relationship/difference between the three-centered, “basket handle” arch, and an ellipse. I have encountered situations when working with wide passages where a true ellipse looks wrong due to the tight radii ends. I guess that probably means the opening was too wide for an arch in the first place :)
Thanks for the wonderfully informative article. As it happens, I have been tasked with fabricating some molding to fit above a bay window-not an arch but an arc none the less. I will certainly use the chord/rise/run formula that you show, so thanks again. Also, I have a nice biography of Fillipo Brunelleschi, the designer and builder of Il Duomo in Milan. The book has a diagram and description of a Gothic arch that is called a quinto arcuto as the layout is derived from 1/5 of the span. The methodology is the same as you describe. Whenever I am tempted to whine about not having some particular tool or skill or material i just look at a Gothic cathedral or a piece of 16th century furniture and go back to work.
Great article Todd!
I love what you do with sketchup.
Wow, just finished with two of the one centered arches, knowing that there was a formula out there. No way to get on the internet at the jobsite, so I used the trial and error method of trying different radius along the centerline until I found the correct one. One guy suggested the old “bend the stick” method, to which I said “no way”. That nite I found the formula and used it to do the second arch. Thanks a million for these articles.
Great article! Thanks for including the downloadable cheatsheets — should be really helpful when trying to walk a crew member through how to create various arches on the jobsite.
Like everyone else, I’m looking forward to your discussion on the 3 center/basket handle/elliptical arch (its a personal favorite!)
Thank you for this valuable resource. I wonder if you might know the answer to a question…I’m a decorator working on a remodel on a 1910 house with some Craftsman influence. The architect has been wanting to insert one-center arched niches and they look wrong to me but I hate to bring it up without doing my research. I tend to associate this shape with homes of a slightly later vintage (1920’s) whereas I often think of gothic or tudor arches in the 1910’s. As much as I like them, I’d prefer to avoid arches altogether on this particular project—we have plenty of other great lines to echo from the original design. But if we use any, I’d like to make sure they are period appropriate. Thoughts?
Hi Wendy, I’m glad you liked the article. I am by NO means an architectural historian, but I have seen examples of various arches used in period Craftsman homes. I know that Gustav Stickley’s periodical of the time, The Craftsman, took the lead in advancing the Arts and Crafts movement. Here is a link to a digital collection.
One of the homes featured in the January 1910 issue incorporates a segmental arch in the interior design. Here is a link.
I am designing a new Arts & Crafts bungalow for my family. I have (3) 3′-0″ wide arches leading to various rooms/hallway and (1) 11′-1″ wide arch between the kitchen and dining room. All (4) arches can be seen from multiple locations, however the small arches are not on the same wall as the large arch. Would you recommend that I keep the rise the same for all arches in this situation? I think it looks okay with a consistent or varied rise, honestly, but I’m a 30 year old structural engineer, not a 50+ year old carpentry expert.
Thank you for your time.
I’m actually half way between 30 and 50, and I certainly don’t have all of the answers… If any at all! :)
The biggest problem I’ve seen in the arch designs used in millwork today is that they are used simply as decorative after thoughts. What could be a focal point of strength and visual support to the design ends up looking like just a curved detail.
Keeping the heights of the arches in a room equal may be necessary because of existing conditions, but don’t sacrifice visual strength just for symmetry. Low rising segmental arches, splayed across a large distance, just tend to look too delicate. Using a depressed arch; like an elliptical, three centered, or pseudo three centered arch will keep the same rise, and still provide symmetry and visual strength for wider openings. Here is an example from Thomas Jefferson’s Map Room at Monticello. One room, two arches, same rise…
Well if Thomas Jefferson can mix arches…
Interesting picture, Todd. I agree with your comments regarding long single circle arches looking delicate, but I think I’m okay with that look. I think what I’m trying to avoid is creating something that’s “wrong” without being aware of it until the drywall is up, at which point it’s too late. I tried attaching a JPG, but I received an error…email??
Do you have instruction for a Pseudo 4-centered or a multicircular arch form?
Part two of this article covers three-centered arches and part three covers the four-centered arches.
Great Article. Very interesting ,Keep it up.
I’m opening a wall between kitchen and living room. The finished opening will be ~14 feet wide. Ceilings are 8 feet. I’d like to add a gradual arch to the opening. Similar to the right-most example in the “Segmental Arches” graphic above. However, I’m not sure where the spring line of the arch should start. Should it be at standard door height of 80″ (6’8″)? Is there a building code that dictates a minimum height at the ends of the arch?
There is a stairway at one end of the opening. So, I want to be sure there is no problem with headroom at the ends of the arch. But, because of the 8′ ceiling, I’m limited by how high I can go at the arch center and still allow for trim (prefer trim look over just drywall opening).
How would you find the arc length for this type of arch?
A construction calculator can also be used to find the arc length of a segmented arch. Here is a link to a Toolbox article that covers it:
hi there, just wondering: is it 110% necessary to have the key stone precisely in the centre? as i am building a bullseye arch that has the keystone centre about 15mm to the right. it still looks fine but just wondering if the whole thing will colllapse on me.
Thank you; Very useful and nicely made.
I want to build an arch in the 5 feet opening in hall entry way. Please let me know suitable arch type? if i choose segmental arch which would proportional rise for 5 feet wide entry way?
I was delighted to come across this article, as I am currently working on a small software application that produces cutting guides and templates for stone arches. I had to relearn all this math and its nice to see how you have presented everything here. At the moment I have just designed the “semi circle” arch algorithm, and have it drawing correctly with any (odd) number of voissours, at any radius, with voissours of any height. The information in this article gives me a great headstart with other types of arch. I often come across this problem during my work as a stonemason. Excellent work my man, you have already waded through it all so I dont have to :)
Thanks for the great article. I found it very useful in my quest to produce a spreadsheet that provides the dimensions of each stone in a single centered arch to surround my half-round window (as well as the inner and outer radius if not using stone). My mission is accomplished, thank you. I hope it can help those with questions about what will fit in their available space and how it will look.
Hi Bill, would you kindly share spreadsheet with me?
It looks like Bill has generously provided access to his spreadsheet AND an online calculator in his comment. To access the link, click on his name in the comment above.
Thank you Bill. Very impressive work!!
Wm. Todd Murdock