FHB Logo Facebook LinkedIn Email Pinterest Twitter X Instagram Tiktok YouTube Plus Icon Close Icon Navigation Search Icon Navigation Search Icon Arrow Down Icon Video Guide Icon Article Guide Icon Modal Close Icon Guide Search Icon Skip to content
Subscribe
Log In
  • How-To
  • Design
  • Tools & Materials
  • Restoration
  • Videos
  • Blogs
  • Forum
  • Magazine
  • Members
  • FHB House
  • Podcast
Log In

Discussion Forum

Discussion Forum

Finding the right radius

silvertip | Posted in Construction Techniques on July 18, 2008 03:56am

Just wanted to know if anyone has a magical way of figuring the right radius for arches.  I have fifteen arches to frame all are different widths from column to column.  At the two ends of where the meet the columns I need them to come down 10 1/2 inches and in the middle 3 1/2 inches.  I have done a few with varying the radius but I would like a mathimatical soultion rather that trial and error on various radii.

Reply
  • X
  • facebook
  • linkedin
  • pinterest
  • email
  • add to favorites Log in or Sign up to save your favorite articles

Replies

  1. Framer | Jul 18, 2008 04:04am | #1

    Do you have a Construction Master calculator?

    Here's one way with any calculator.

     (1/2 Chord x² / H) + H (/ 2) = Radius

    Joe Carola



    Edited 7/17/2008 9:10 pm ET by Framer

  2. DougU | Jul 18, 2008 05:19am | #2

    ((1/2C)² + h²)/2h

    Sorry, I see Joe already posted it



    Edited 7/17/2008 10:21 pm ET by DougU

  3. HammerHarry | Jul 18, 2008 05:48am | #3

    It depends on if you want a true semi-circle, as implied by the 'radius' term, or if you're looking for an eliptical arch, which may look better, depending on the style you're looking for.

    I think there have been several threads dealing with elipses and arches.

  4. JoeBartok | Jul 18, 2008 06:51pm | #4

    Circle Calculators ... that's probably more than you ever wanted to know about circles. :)

    If your arch is an ellipse (probably not, since you are looking for a radius):

    Elliptical Arch ... known: Major or Minor Axis

    Elliptical Arch ... known: Two Arch Dimensions

    Elliptical Arch ... known: Two Points on the Ellipse

    If the curve is some other conic section (or any other known curve), holler ...

    Joe Bartok


    Edited 7/18/2008 11:58 am ET by JoeBartok



    Edited 7/18/2008 11:59 am ET by JoeBartok

    1. silvertip | Jul 19, 2008 02:30am | #5

      Thanks, will give it a shot. 

      1. Framer | Jul 19, 2008 02:34am | #6

        What are some of the widths if you don't mind me asking?

        Do you have a Construction Master Calculator?

         

         Joe Carola

        1. silvertip | Jul 19, 2008 07:25pm | #11

          I did one with a witdh of 128 3/4" and the radius was 25' 9" which almost work perfect.  I think the middle was off by a 1/4" which was  easy  to fudged.  Will post a few pics when I get back to work on Monday.

          Edited 7/19/2008 12:29 pm ET by silvertip

          1. Framer | Jul 19, 2008 09:22pm | #14

            I did one with a witdh of 128 3/4" and the radius was 25' 9" which almost work perfect. 

            Those measurements would give you a 6-3/4" rise.

            128-3/4" [Run]

            25' 9" [Conv] [Diag]

            [Rise] = 6-3/4" or 6.780114"

            Watch how a few changed numbers in the decimals gives you a different radius by taking the 6.780114" and using that compared to the 6-3/4" number.

            6.780114" [Rise]

            128-3/4" [Run]

            [Conv] [Diag] = 25' 9" = Radius

            Now using 6-3/4"

            6 -3/4" [Rise]

            128-3/4" [Run]

            [Conv] [Diag] = 310-3/8" or 25' 10-3/8" = Radius

            If you have to use 7" as your rise for all the openings like I thought you did in your first post.

            128-3/4" [Run]

            7" [Rise]

            [Conv] [Diag] = 299-1/2" or 24'11-1/2" = Radius

             Joe Carola

    2. mathewson | Jul 19, 2008 05:06am | #7

      Joe,I have to lay out and elliptical stair well Monday. This webpages of yours will help.Thanks,Keith

      1. User avater
        Timuhler | Jul 19, 2008 06:15pm | #10

        Please post pictures of the process or just some here and there.  I'd love to watch the progress

  5. Captndestructo | Jul 19, 2008 03:10pm | #8

    I use a construction calculator for everything i possibly can but I was not aware I could use it to find the radius of a circle.  I am slightly confused by the calculations submitted.  (I am easily confused)  I will read the manual further to understand the calculations.   I always find the radius with two tape measures.  Pull one tape from the high point and one tape from the low point (properly spaced ).  Intersect the tapes, when the number is the same you have your radius.

    1. Framer | Jul 19, 2008 05:02pm | #9

      Sounds like he's coming down from the ceiling on the ends 1-1/2' and in the center 3-1/2" from the ceiling. That would give him 7" from the bottom of the 10/12" up to the center.

      I'm using the Construction Master Pro DT (Desktop) for this.

      Ket's say he has 6' for the width(chord) and 7" for the height.

      6' [Run]

      7" [Rise]

      [Conv] [Diag] = 96 1/6" = Radius

      Or:

      (1/2 Chord x² / H) + H (/ 2) = Radius

      36x² = 1296÷ 7= 185.1429 + 7 = 192.1429 ÷ 2 = 96.07143" or 96 1/16"

      Joe Carola

      Edited 7/19/2008 10:20 am ET by Framer

      1. Captndestructo | Jul 19, 2008 07:47pm | #12

        Thanks.  I honestly have to find the proper radius for something atleast 3 out of 5 days a week.  This will make it go a lot faster

        1. joewood | Jul 19, 2008 07:59pm | #13

          I don't know if you have SketchUp, but it's one quick way of finding radius's :-)http://woodsshop.com/

Log in or create an account to post a comment.

Sign up Log in

Become a member and get full access to FineHomebuilding.com

Video Shorts

Categories

  • Business
  • Code Questions
  • Construction Techniques
  • Energy, Heating & Insulation
  • General Discussion
  • Help/Work Wanted
  • Photo Gallery
  • Reader Classified
  • Tools for Home Building

Discussion Forum

Recent Posts and Replies

  • |
  • |
  • |
  • |
  • |
  • |
View More Create Post

Up Next

Video Shorts

Featured Story

Podcast Episode 693: Old-House Hazards, Building Larsen Trusses, AI in Construction

The crew talks about work start times, fire-resistant construction, fixer-uppers, building Larsen trusses, and AI for construction.

Featured Video

Micro-Adjust Deck-Baluster Spacing for an Eye-Deceiving Layout

No math, no measuring—just a simple jig made from an elastic band is all you need to lay out a good-looking deck railing.

Related Stories

  • Podcast Episode 693: Old-House Hazards, Building Larsen Trusses, AI in Construction
  • FHB Podcast Segment: Finding Hazardous Materials in a Fixer-Upper
  • A Classic Paint Sprayer Gets a Thoughtful Refresh
  • Podcast Episode 692: Introduction to Trade Work, Embodied Carbon, and Envelope Improvements

Highlights

Fine Homebuilding All Access
Fine Homebuilding Podcast
Tool Tech
Plus, get an extra 20% off with code GIFT20

"I have learned so much thanks to the searchable articles on the FHB website. I can confidently say that I expect to be a life-long subscriber." - M.K.

Get home building tips, offers, and expert advice in your inbox

Signing you up...

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
See all newsletters
See all newsletters

Fine Homebuilding Magazine

  • Issue 332 - July 2025
    • Custom Built-ins With Job-Site Tools
    • Fight House Fires Through Design
    • Making the Move to Multifamily
  • Issue 331 - June 2025
    • A More Resilient Roof
    • Tool Test: You Need a Drywall Sander
    • Ducted vs. Ductless Heat Pumps
  • Issue 330 - April/May 2025
    • Deck Details for Durability
    • FAQs on HPWHs
    • 10 Tips for a Long-Lasting Paint Job
  • Issue 329 - Feb/Mar 2025
    • Smart Foundation for a Small Addition
    • A Kominka Comes West
    • Making Small Kitchens Work
  • Issue 328 - Dec/Jan 2025
    • How a Pro Replaces Columns
    • Passive House 3.0
    • Tool Test: Compact Line Lasers

Fine Home Building

Newsletter Sign-up

  • Fine Homebuilding

    Home building tips, offers, and expert advice in your inbox.

  • Green Building Advisor

    Building science and energy efficiency advice, plus special offers, in your inbox.

  • Old House Journal

    Repair, renovation, and restoration tips, plus special offers, in your inbox.

Signing you up...

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
See all newsletters

Follow

  • Fine Homebuilding

    Dig into cutting-edge approaches and decades of proven solutions with total access to our experts and tradespeople.

    Start Free Trial Now
    • Facebook
    • Instagram
    • X
    • LinkedIn
  • GBA Prime

    Get instant access to the latest developments in green building, research, and reports from the field.

    Start Free Trial Now
    • Facebook
    • YouTube
  • Old House Journal

    Learn how to restore, repair, update, and decorate your home.

    Subscribe Now
    • Facebook
    • Instagram
    • X
  • Fine Homebuilding

    Dig into cutting-edge approaches and decades of proven solutions with total access to our experts and tradespeople.

    Start Free Trial Now
    • Facebook
    • Instagram
    • X
    • LinkedIn
  • GBA Prime

    Get instant access to the latest developments in green building, research, and reports from the field.

    Start Free Trial Now
    • Facebook
    • YouTube
  • Old House Journal

    Learn how to restore, repair, update, and decorate your home.

    Subscribe Now
    • Facebook
    • Instagram
    • X

Membership & Magazine

  • Online Archive
  • Start Free Trial
  • Magazine Subscription
  • Magazine Renewal
  • Gift a Subscription
  • Customer Support
  • Privacy Preferences
  • About
  • Contact
  • Advertise
  • Careers
  • Terms of Use
  • Site Map
  • Do not sell or share my information
  • Privacy Policy
  • Accessibility
  • California Privacy Rights

© 2025 Active Interest Media. All rights reserved.

Fine Homebuilding receives a commission for items purchased through links on this site, including Amazon Associates and other affiliate advertising programs.

  • Home Group
  • Antique Trader
  • Arts & Crafts Homes
  • Bank Note Reporter
  • Cabin Life
  • Cuisine at Home
  • Fine Gardening
  • Fine Woodworking
  • Green Building Advisor
  • Garden Gate
  • Horticulture
  • Keep Craft Alive
  • Log Home Living
  • Military Trader/Vehicles
  • Numismatic News
  • Numismaster
  • Old Cars Weekly
  • Old House Journal
  • Period Homes
  • Popular Woodworking
  • Script
  • ShopNotes
  • Sports Collectors Digest
  • Threads
  • Timber Home Living
  • Traditional Building
  • Woodsmith
  • World Coin News
  • Writer's Digest
Active Interest Media logo
X
X
This is a dialog window which overlays the main content of the page. The modal window is a 'site map' of the most critical areas of the site. Pressing the Escape (ESC) button will close the modal and bring you back to where you were on the page.

Main Menu

  • How-To
  • Design
  • Tools & Materials
  • Video
  • Blogs
  • Forum
  • Project Guides
  • Reader Projects
  • Magazine
  • Members
  • FHB House

Podcasts

  • FHB Podcast
  • ProTalk

Webinars

  • Upcoming and On-Demand

Podcasts

  • FHB Podcast
  • ProTalk

Webinars

  • Upcoming and On-Demand

Popular Topics

  • Kitchens
  • Business
  • Bedrooms
  • Roofs
  • Architecture and Design
  • Green Building
  • Decks
  • Framing
  • Safety
  • Remodeling
  • Bathrooms
  • Windows
  • Tilework
  • Ceilings
  • HVAC

Magazine

  • Current Issue
  • Past Issues
  • Magazine Index
  • Subscribe
  • Online Archive
  • Author Guidelines

All Access

  • Member Home
  • Start Free Trial
  • Gift Membership

Online Learning

  • Courses
  • Project Guides
  • Reader Projects
  • Podcast

More

  • FHB Ambassadors
  • FHB House
  • Customer Support

Account

  • Log In
  • Join

Newsletter

Get home building tips, offers, and expert advice in your inbox

Signing you up...

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
See all newsletters
See all newsletters

Follow

  • X
  • YouTube
  • instagram
  • facebook
  • pinterest
  • Tiktok

Join All Access

Become a member and get instant access to thousands of videos, how-tos, tool reviews, and design features.

Start Your Free Trial

Subscribe

FHB Magazine

Start your subscription today and save up to 70%

Subscribe

Enjoy unlimited access to Fine Homebuilding. Join Now

Already a member? Log in

We hope you’ve enjoyed your free articles. To keep reading, become a member today.

Get complete site access to expert advice, how-to videos, Code Check, and more, plus the print magazine.

Start your FREE trial

Already a member? Log in

Privacy Policy Update

We use cookies, pixels, script and other tracking technologies to analyze and improve our service, to improve and personalize content, and for advertising to you. We also share information about your use of our site with third-party social media, advertising and analytics partners. You can view our Privacy Policy here and our Terms of Use here.

Cookies

Analytics

These cookies help us track site metrics to improve our sites and provide a better user experience.

Advertising/Social Media

These cookies are used to serve advertisements aligned with your interests.

Essential

These cookies are required to provide basic functions like page navigation and access to secure areas of the website.

Delete My Data

Delete all cookies and associated data